diff --git a/packages/core/src/routes/interaction/utils/single-sign-on.test.ts b/packages/core/src/routes/interaction/utils/single-sign-on.test.ts
index 27dad1929..118041021 100644
--- a/packages/core/src/routes/interaction/utils/single-sign-on.test.ts
+++ b/packages/core/src/routes/interaction/utils/single-sign-on.test.ts
@@ -1,4 +1,3 @@
-import { type SsoConnector } from '@logto/schemas';
 import { createMockUtils } from '@logto/shared/esm';
 import type Provider from 'oidc-provider';
 
@@ -7,6 +6,7 @@ import RequestError from '#src/errors/RequestError/index.js';
 import { type WithLogContext } from '#src/middleware/koa-audit-log.js';
 import { OidcSsoConnector } from '#src/sso/OidcSsoConnector/index.js';
 import { ssoConnectorFactories } from '#src/sso/index.js';
+import { type SingleSignOnConnectorData } from '#src/sso/types/index.js';
 import { createMockLogContext } from '#src/test-utils/koa-audit-log.js';
 import { createMockProvider } from '#src/test-utils/oidc-provider.js';
 import { MockTenant } from '#src/test-utils/tenant.js';
@@ -49,7 +49,7 @@ const {
 
 jest
   .spyOn(ssoConnectorFactories.OIDC, 'constructor')
-  .mockImplementation((data: SsoConnector) => new MockOidcSsoConnector(data));
+  .mockImplementation((data: SingleSignOnConnectorData) => new MockOidcSsoConnector(data));
 
 const {
   getSsoAuthorizationUrl,
diff --git a/packages/core/src/routes/sso-connector/index.ts b/packages/core/src/routes/sso-connector/index.ts
index 40781e098..d0b07bbc7 100644
--- a/packages/core/src/routes/sso-connector/index.ts
+++ b/packages/core/src/routes/sso-connector/index.ts
@@ -24,6 +24,7 @@ import {
   parseConnectorConfig,
   fetchConnectorProviderDetails,
   validateConnectorDomains,
+  validateConnectorConfigConnectionStatus,
 } from './utils.js';
 
 export default function singleSignOnRoutes<T extends AuthedRouter>(...args: RouterInitArgs<T>) {
@@ -89,7 +90,7 @@ export default function singleSignOnRoutes<T extends AuthedRouter>(...args: Rout
     }),
     async (ctx, next) => {
       const { body } = ctx.guard;
-      const { providerName, connectorName, config, ...rest } = body;
+      const { providerName, connectorName, config, domains, ...rest } = body;
 
       // Return 422 if the connector provider is not supported
       if (!isSupportedSsoProvider(providerName)) {
@@ -101,17 +102,33 @@ export default function singleSignOnRoutes<T extends AuthedRouter>(...args: Rout
       }
 
       // Validate the connector domains if it's provided
-      validateConnectorDomains(rest.domains);
+      if (domains) {
+        validateConnectorDomains(domains);
+      }
 
       // Validate the connector config if it's provided
       const parsedConfig = config && parseConnectorConfig(providerName, config);
 
       const connectorId = generateStandardShortId();
+
+      // Check the connection status of the connector config if it's provided
+      if (parsedConfig) {
+        await validateConnectorConfigConnectionStatus(
+          {
+            id: connectorId,
+            providerName,
+            config: parsedConfig,
+          },
+          tenantId
+        );
+      }
+
       const connector = await ssoConnectors.insert({
         id: connectorId,
         providerName,
         connectorName,
         ...conditional(config && { config: parsedConfig }),
+        ...conditional(domains && { domains }),
         ...rest,
       });
 
@@ -200,14 +217,28 @@ export default function singleSignOnRoutes<T extends AuthedRouter>(...args: Rout
 
       const originalConnector = await getSsoConnectorById(id);
       const { providerName } = originalConnector;
-      const { config, ...rest } = body;
+      const { config, domains, ...rest } = body;
 
       // Validate the connector domains if it's provided
-      validateConnectorDomains(rest.domains);
+      if (domains) {
+        validateConnectorDomains(domains);
+      }
 
       // Validate the connector config if it's provided
       const parsedConfig = config && parseConnectorConfig(providerName, config);
 
+      // Check the connection status of the connector config if it's provided
+      if (parsedConfig) {
+        await validateConnectorConfigConnectionStatus(
+          {
+            id,
+            providerName,
+            config: parsedConfig,
+          },
+          tenantId
+        );
+      }
+
       // Check if there's any valid update
       const hasValidUpdate = parsedConfig ?? Object.keys(rest).length > 0;
 
@@ -215,6 +246,7 @@ export default function singleSignOnRoutes<T extends AuthedRouter>(...args: Rout
       const connector = hasValidUpdate
         ? await ssoConnectors.updateById(id, {
             ...conditional(parsedConfig && { config: parsedConfig }),
+            ...conditional(domains && { domains }),
             ...rest,
           })
         : originalConnector;
diff --git a/packages/core/src/routes/sso-connector/utils.test.ts b/packages/core/src/routes/sso-connector/utils.test.ts
index 0504e0e78..64a35e593 100644
--- a/packages/core/src/routes/sso-connector/utils.test.ts
+++ b/packages/core/src/routes/sso-connector/utils.test.ts
@@ -106,12 +106,6 @@ describe('fetchConnectorProviderDetails', () => {
 });
 
 describe('validateConnectorDomains', () => {
-  it('should directly return if domains are not provided', () => {
-    expect(() => {
-      validateConnectorDomains();
-    }).not.toThrow();
-  });
-
   it('should directly return if domains are empty', () => {
     expect(() => {
       validateConnectorDomains([]);
diff --git a/packages/core/src/routes/sso-connector/utils.ts b/packages/core/src/routes/sso-connector/utils.ts
index 660db46ef..d676b0ee9 100644
--- a/packages/core/src/routes/sso-connector/utils.ts
+++ b/packages/core/src/routes/sso-connector/utils.ts
@@ -9,7 +9,9 @@ import { findDuplicatedOrBlockedEmailDomains } from '@logto/schemas';
 import { trySafe } from '@silverhand/essentials';
 
 import RequestError from '#src/errors/RequestError/index.js';
+import SamlConnector from '#src/sso/SamlConnector/index.js';
 import { type SingleSignOnFactory, ssoConnectorFactories } from '#src/sso/index.js';
+import { type SingleSignOnConnectorData } from '#src/sso/types/index.js';
 
 const isKeyOfI18nPhrases = (key: string, phrases: I18nPhrases): key is keyof I18nPhrases =>
   key in phrases;
@@ -75,6 +77,27 @@ export const fetchConnectorProviderDetails = async (
   };
 };
 
+/**
+ * Validate the connector config.
+ * Fetch or parse the connector IdP detailed settings using the connector config.
+ * Throw error if the connector config is invalid.
+ */
+export const validateConnectorConfigConnectionStatus = async (
+  connector: SingleSignOnConnectorData,
+  tenantId: string
+) => {
+  const { providerName } = connector;
+  const { constructor } = ssoConnectorFactories[providerName];
+  const instance = new constructor(connector, tenantId);
+
+  // SAML connector's idpMetadata is optional (safely catch by the getConfig method), we need to force fetch the IdP metadata here
+  if (instance instanceof SamlConnector) {
+    return instance.getSamlIdpMetadata();
+  }
+
+  return instance.getConfig();
+};
+
 /**
  * Validate the connector domains using the domain blacklist.
  * - Throw error if the domains are invalid.
@@ -83,7 +106,7 @@ export const fetchConnectorProviderDetails = async (
  * @param domains
  * @returns
  */
-export const validateConnectorDomains = (domains?: string[]) => {
+export const validateConnectorDomains = (domains: string[]) => {
   const { duplicatedDomains, forbiddenDomains } = findDuplicatedOrBlockedEmailDomains(domains);
 
   if (forbiddenDomains.size > 0) {
diff --git a/packages/core/src/sso/GoogleWorkspaceSsoConnector/index.ts b/packages/core/src/sso/GoogleWorkspaceSsoConnector/index.ts
index 1b8b27968..076517b78 100644
--- a/packages/core/src/sso/GoogleWorkspaceSsoConnector/index.ts
+++ b/packages/core/src/sso/GoogleWorkspaceSsoConnector/index.ts
@@ -1,9 +1,13 @@
 import { ConnectorError, ConnectorErrorCodes } from '@logto/connector-kit';
-import { type SsoConnector, SsoProviderName } from '@logto/schemas';
+import { SsoProviderName } from '@logto/schemas';
 
 import OidcConnector from '../OidcConnector/index.js';
 import { type SingleSignOnFactory } from '../index.js';
-import { type CreateSingleSignOnSession, type SingleSignOn } from '../types/index.js';
+import {
+  type CreateSingleSignOnSession,
+  type SingleSignOn,
+  type SingleSignOnConnectorData,
+} from '../types/index.js';
 import { basicOidcConnectorConfigGuard } from '../types/oidc.js';
 
 // Google use static issue endpoint.
@@ -12,7 +16,7 @@ const googleIssuer = 'https://accounts.google.com';
 export class GoogleWorkspaceSsoConnector extends OidcConnector implements SingleSignOn {
   static googleIssuer = googleIssuer;
 
-  constructor(readonly data: SsoConnector) {
+  constructor(readonly data: SingleSignOnConnectorData) {
     const parseConfigResult = googleWorkspaceSsoConnectorConfigGuard.safeParse(data.config);
 
     if (!parseConfigResult.success) {
diff --git a/packages/core/src/sso/OidcConnector/index.ts b/packages/core/src/sso/OidcConnector/index.ts
index f74480f74..f0c3d3d7b 100644
--- a/packages/core/src/sso/OidcConnector/index.ts
+++ b/packages/core/src/sso/OidcConnector/index.ts
@@ -1,6 +1,5 @@
-import { ConnectorError, ConnectorErrorCodes } from '@logto/connector-kit';
 import { generateStandardId } from '@logto/shared/universal';
-import { assert, conditional } from '@silverhand/essentials';
+import { conditional } from '@silverhand/essentials';
 import snakecaseKeys from 'snakecase-keys';
 
 import {
@@ -62,13 +61,6 @@ class OidcConnector {
     setSession: CreateSingleSignOnSession,
     prompt?: 'login' | 'consent' | 'none' | 'select_account'
   ) {
-    assert(
-      setSession,
-      new ConnectorError(ConnectorErrorCodes.NotImplemented, {
-        message: 'Connector session storage is not implemented.',
-      })
-    );
-
     const oidcConfig = await this.getOidcConfig();
     const nonce = generateStandardId();
 
diff --git a/packages/core/src/sso/OidcConnector/utils.test.ts b/packages/core/src/sso/OidcConnector/utils.test.ts
index 306236032..3e5dc1f73 100644
--- a/packages/core/src/sso/OidcConnector/utils.test.ts
+++ b/packages/core/src/sso/OidcConnector/utils.test.ts
@@ -1,7 +1,11 @@
-import { ConnectorError, ConnectorErrorCodes } from '@logto/connector-kit';
 import { createMockUtils } from '@logto/shared/esm';
 import camelcaseKeys from 'camelcase-keys';
 
+import {
+  SsoConnectorConfigErrorCodes,
+  SsoConnectorError,
+  SsoConnectorErrorCodes,
+} from '../types/error.js';
 import {
   oidcConfigResponseGuard,
   oidcAuthorizationResponseGuard,
@@ -48,7 +52,11 @@ describe('fetchOidcConfig', () => {
     getMock.mockRejectedValueOnce(new MockHttpError({ body: 'invalid endpoint' }));
 
     await expect(fetchOidcConfig(issuer)).rejects.toMatchError(
-      new ConnectorError(ConnectorErrorCodes.General, 'invalid endpoint')
+      new SsoConnectorError(SsoConnectorErrorCodes.InvalidConfig, {
+        config: { issuer },
+        message: SsoConnectorConfigErrorCodes.FailToFetchConfig,
+        error: 'invalid endpoint',
+      })
     );
     expect(getMock).toBeCalledWith(`${issuer}/.well-known/openid-configuration`, {
       responseType: 'json',
@@ -71,7 +79,11 @@ describe('fetchOidcConfig', () => {
     }
 
     await expect(fetchOidcConfig(issuer)).rejects.toMatchError(
-      new ConnectorError(ConnectorErrorCodes.InvalidConfig, result.error)
+      new SsoConnectorError(SsoConnectorErrorCodes.InvalidConfig, {
+        config: { issuer },
+        message: SsoConnectorConfigErrorCodes.InvalidConfigResponse,
+        error: result.error.flatten(),
+      })
     );
   });
 
@@ -117,7 +129,13 @@ describe('fetchToken', () => {
         data,
         redirectUri
       )
-    ).rejects.toMatchError(new ConnectorError(ConnectorErrorCodes.General, result.error));
+    ).rejects.toMatchError(
+      new SsoConnectorError(SsoConnectorErrorCodes.InvalidRequestParameters, {
+        url: oidcConfigResponseCamelCase.tokenEndpoint,
+        params: data,
+        error: result.error.flatten(),
+      })
+    );
 
     expect(postMock).not.toBeCalled();
   });
@@ -134,7 +152,12 @@ describe('fetchToken', () => {
         data,
         redirectUri
       )
-    ).rejects.toMatchError(new ConnectorError(ConnectorErrorCodes.General, 'invalid response'));
+    ).rejects.toMatchError(
+      new SsoConnectorError(SsoConnectorErrorCodes.AuthorizationFailed, {
+        message: 'Fail to fetch token',
+        error: 'invalid response',
+      })
+    );
 
     expect(postMock).toBeCalledWith({
       url: oidcConfigResponseCamelCase.tokenEndpoint,
@@ -169,7 +192,13 @@ describe('fetchToken', () => {
         data,
         redirectUri
       )
-    ).rejects.toMatchError(new ConnectorError(ConnectorErrorCodes.InvalidResponse, result.error));
+    ).rejects.toMatchError(
+      new SsoConnectorError(SsoConnectorErrorCodes.AuthorizationFailed, {
+        message: 'Invalid token response',
+        response: JSON.stringify(body),
+        error: result.error.flatten(),
+      })
+    );
   });
 
   it('should return the token response if the token endpoint returns valid response', async () => {
diff --git a/packages/core/src/sso/OidcConnector/utils.ts b/packages/core/src/sso/OidcConnector/utils.ts
index 68ba78f85..8d6422a59 100644
--- a/packages/core/src/sso/OidcConnector/utils.ts
+++ b/packages/core/src/sso/OidcConnector/utils.ts
@@ -1,10 +1,15 @@
-import { ConnectorError, ConnectorErrorCodes, parseJson } from '@logto/connector-kit';
+import { parseJson } from '@logto/connector-kit';
 import { assert } from '@silverhand/essentials';
 import camelcaseKeys, { type CamelCaseKeys } from 'camelcase-keys';
 import { got, HTTPError } from 'got';
 import { jwtVerify, createRemoteJWKSet } from 'jose';
 import { z } from 'zod';
 
+import {
+  SsoConnectorError,
+  SsoConnectorErrorCodes,
+  SsoConnectorConfigErrorCodes,
+} from '../types/error.js';
 import {
   type BaseOidcConfig,
   type OidcConfigResponse,
@@ -26,15 +31,24 @@ export const fetchOidcConfig = async (
     const result = oidcConfigResponseGuard.safeParse(body);
 
     if (!result.success) {
-      throw new ConnectorError(ConnectorErrorCodes.InvalidConfig, result.error);
+      throw new SsoConnectorError(SsoConnectorErrorCodes.InvalidConfig, {
+        config: { issuer },
+        message: SsoConnectorConfigErrorCodes.InvalidConfigResponse,
+        error: result.error.flatten(),
+      });
     }
 
     return camelcaseKeys(result.data);
   } catch (error: unknown) {
-    if (error instanceof HTTPError) {
-      throw new ConnectorError(ConnectorErrorCodes.General, error.response.body);
+    if (error instanceof SsoConnectorError) {
+      throw error;
     }
-    throw error;
+
+    throw new SsoConnectorError(SsoConnectorErrorCodes.InvalidConfig, {
+      config: { issuer },
+      message: SsoConnectorConfigErrorCodes.FailToFetchConfig,
+      error: error instanceof HTTPError ? error.response.body : error,
+    });
   }
 };
 
@@ -46,7 +60,11 @@ export const fetchToken = async (
   const result = oidcAuthorizationResponseGuard.safeParse(data);
 
   if (!result.success) {
-    throw new ConnectorError(ConnectorErrorCodes.General, result.error);
+    throw new SsoConnectorError(SsoConnectorErrorCodes.InvalidRequestParameters, {
+      url: tokenEndpoint,
+      params: data,
+      error: result.error.flatten(),
+    });
   }
 
   const { code } = result.data;
@@ -66,15 +84,23 @@ export const fetchToken = async (
     const result = oidcTokenResponseGuard.safeParse(parseJson(httpResponse.body));
 
     if (!result.success) {
-      throw new ConnectorError(ConnectorErrorCodes.InvalidResponse, result.error);
+      throw new SsoConnectorError(SsoConnectorErrorCodes.AuthorizationFailed, {
+        message: 'Invalid token response',
+        response: httpResponse.body,
+        error: result.error.flatten(),
+      });
     }
 
     return camelcaseKeys(result.data);
   } catch (error: unknown) {
-    if (error instanceof HTTPError) {
-      throw new ConnectorError(ConnectorErrorCodes.General, error.response.body);
+    if (error instanceof SsoConnectorError) {
+      throw error;
     }
-    throw error;
+
+    throw new SsoConnectorError(SsoConnectorErrorCodes.AuthorizationFailed, {
+      message: 'Fail to fetch token',
+      error: error instanceof HTTPError ? error.response.body : error,
+    });
   }
 };
 
@@ -92,13 +118,19 @@ export const getIdTokenClaims = async (
     });
 
     if (Math.abs((payload.iat ?? 0) - Date.now() / 1000) > issuedAtTimeTolerance) {
-      throw new ConnectorError(ConnectorErrorCodes.SocialIdTokenInvalid, 'id_token is expired');
+      throw new SsoConnectorError(SsoConnectorErrorCodes.AuthorizationFailed, {
+        message: 'id_token is expired',
+        response: payload,
+      });
     }
 
     const result = idTokenProfileStandardClaimsGuard.safeParse(payload);
 
     if (!result.success) {
-      throw new ConnectorError(ConnectorErrorCodes.SocialIdTokenInvalid, result.error);
+      throw new SsoConnectorError(SsoConnectorErrorCodes.AuthorizationFailed, {
+        message: 'invalid id_token',
+        response: payload,
+      });
     }
 
     const { data } = result;
@@ -106,16 +138,21 @@ export const getIdTokenClaims = async (
     if (data.nonce) {
       assert(
         data.nonce === nonceFromSession,
-        new ConnectorError(ConnectorErrorCodes.SocialIdTokenInvalid, 'nonce claim not match')
+        new SsoConnectorError(SsoConnectorErrorCodes.AuthorizationFailed, {
+          message: 'nonce does not match',
+        })
       );
     }
 
     return data;
   } catch (error: unknown) {
-    if (error instanceof ConnectorError) {
+    if (error instanceof SsoConnectorError) {
       throw error;
     }
-    throw new ConnectorError(ConnectorErrorCodes.SocialIdTokenInvalid, error);
+    throw new SsoConnectorError(SsoConnectorErrorCodes.AuthorizationFailed, {
+      message: 'Fail to verify id_token',
+      error,
+    });
   }
 };
 
@@ -136,16 +173,24 @@ export const getUserInfo = async (accessToken: string, userinfoEndpoint: string)
       .safeParse(httpResponse.body);
 
     if (!result.success) {
-      throw new ConnectorError(ConnectorErrorCodes.InvalidResponse, result.error);
+      throw new SsoConnectorError(SsoConnectorErrorCodes.AuthorizationFailed, {
+        message: 'Invalid user info response',
+        response: httpResponse.body,
+        error: result.error.flatten(),
+      });
     }
 
     const { data } = result;
 
     return data;
   } catch (error: unknown) {
-    if (error instanceof HTTPError) {
-      throw new ConnectorError(ConnectorErrorCodes.General, error.response.body);
+    if (error instanceof SsoConnectorError) {
+      throw error;
     }
-    throw error;
+
+    throw new SsoConnectorError(SsoConnectorErrorCodes.AuthorizationFailed, {
+      message: 'Fail to fetch user info',
+      error: error instanceof HTTPError ? error.response.body : error,
+    });
   }
 };
diff --git a/packages/core/src/sso/OidcSsoConnector/index.test.ts b/packages/core/src/sso/OidcSsoConnector/index.test.ts
index c0c06c074..0e07f6f97 100644
--- a/packages/core/src/sso/OidcSsoConnector/index.test.ts
+++ b/packages/core/src/sso/OidcSsoConnector/index.test.ts
@@ -1,8 +1,13 @@
-import { ConnectorError, ConnectorErrorCodes } from '@logto/connector-kit';
 import { SsoProviderName } from '@logto/schemas';
 
 import { mockSsoConnector } from '#src/__mocks__/sso.js';
 
+import {
+  SsoConnectorError,
+  SsoConnectorErrorCodes,
+  SsoConnectorConfigErrorCodes,
+} from '../types/error.js';
+
 import { oidcSsoConnectorFactory } from './index.js';
 
 describe('OidcSsoConnector', () => {
@@ -23,7 +28,11 @@ describe('OidcSsoConnector', () => {
     };
 
     expect(createOidcSsoConnector).toThrow(
-      new ConnectorError(ConnectorErrorCodes.InvalidConfig, result.error)
+      new SsoConnectorError(SsoConnectorErrorCodes.InvalidConfig, {
+        config: mockSsoConnector.config,
+        message: SsoConnectorConfigErrorCodes.InvalidConnectorConfig,
+        error: result.error.flatten(),
+      })
     );
   });
 });
diff --git a/packages/core/src/sso/OidcSsoConnector/index.ts b/packages/core/src/sso/OidcSsoConnector/index.ts
index db8cf028a..808d31db5 100644
--- a/packages/core/src/sso/OidcSsoConnector/index.ts
+++ b/packages/core/src/sso/OidcSsoConnector/index.ts
@@ -1,17 +1,25 @@
-import { ConnectorError, ConnectorErrorCodes } from '@logto/connector-kit';
-import { type SsoConnector, SsoProviderName } from '@logto/schemas';
+import { SsoProviderName } from '@logto/schemas';
 
 import OidcConnector from '../OidcConnector/index.js';
 import { type SingleSignOnFactory } from '../index.js';
-import { type SingleSignOn } from '../types/index.js';
+import {
+  SsoConnectorError,
+  SsoConnectorErrorCodes,
+  SsoConnectorConfigErrorCodes,
+} from '../types/error.js';
+import { type SingleSignOn, type SingleSignOnConnectorData } from '../types/index.js';
 import { basicOidcConnectorConfigGuard } from '../types/oidc.js';
 
 export class OidcSsoConnector extends OidcConnector implements SingleSignOn {
-  constructor(readonly data: SsoConnector) {
+  constructor(readonly data: SingleSignOnConnectorData) {
     const parseConfigResult = basicOidcConnectorConfigGuard.safeParse(data.config);
 
     if (!parseConfigResult.success) {
-      throw new ConnectorError(ConnectorErrorCodes.InvalidConfig, parseConfigResult.error);
+      throw new SsoConnectorError(SsoConnectorErrorCodes.InvalidConfig, {
+        config: data.config,
+        message: SsoConnectorConfigErrorCodes.InvalidConnectorConfig,
+        error: parseConfigResult.error.flatten(),
+      });
     }
 
     super(parseConfigResult.data);
diff --git a/packages/core/src/sso/OktaSsoConnector/index.ts b/packages/core/src/sso/OktaSsoConnector/index.ts
index 625f8cd99..1bc750043 100644
--- a/packages/core/src/sso/OktaSsoConnector/index.ts
+++ b/packages/core/src/sso/OktaSsoConnector/index.ts
@@ -1,4 +1,3 @@
-import { ConnectorError, ConnectorErrorCodes } from '@logto/connector-kit';
 import { SsoProviderName } from '@logto/schemas';
 import { conditional } from '@silverhand/essentials';
 import camelcaseKeys from 'camelcase-keys';
@@ -8,6 +7,7 @@ import assertThat from '#src/utils/assert-that.js';
 import { fetchToken, getUserInfo, getIdTokenClaims } from '../OidcConnector/utils.js';
 import { OidcSsoConnector } from '../OidcSsoConnector/index.js';
 import { type SingleSignOnFactory } from '../index.js';
+import { SsoConnectorError, SsoConnectorErrorCodes } from '../types/error.js';
 import { basicOidcConnectorConfigGuard } from '../types/oidc.js';
 import { type ExtendedSocialUserInfo } from '../types/saml.js';
 import { type SingleSignOnConnectorSession } from '../types/session.js';
@@ -33,7 +33,9 @@ export class OktaSsoConnector extends OidcSsoConnector {
 
     assertThat(
       accessToken,
-      new ConnectorError(ConnectorErrorCodes.AuthorizationFailed, 'access_token is empty.')
+      new SsoConnectorError(SsoConnectorErrorCodes.AuthorizationFailed, {
+        message: 'The access token is missing from the response.',
+      })
     );
 
     // Verify the id token and get the user id
diff --git a/packages/core/src/sso/SamlConnector/index.ts b/packages/core/src/sso/SamlConnector/index.ts
index e061cd7b0..d1b61ab3b 100644
--- a/packages/core/src/sso/SamlConnector/index.ts
+++ b/packages/core/src/sso/SamlConnector/index.ts
@@ -1,10 +1,14 @@
-import { ConnectorError, ConnectorErrorCodes } from '@logto/connector-kit';
 import { type Optional } from '@silverhand/essentials';
 import * as saml from 'samlify';
 import { z } from 'zod';
 
 import { EnvSet, getTenantEndpoint } from '#src/env-set/index.js';
 
+import {
+  SsoConnectorConfigErrorCodes,
+  SsoConnectorError,
+  SsoConnectorErrorCodes,
+} from '../types/error.js';
 import {
   type SamlConnectorConfig,
   type ExtendedSocialUserInfo,
@@ -83,7 +87,10 @@ class SamlConnector {
    */
   get idpConfig() {
     if (!this._idpConfig) {
-      throw new ConnectorError(ConnectorErrorCodes.InvalidConfig, 'config not found');
+      throw new SsoConnectorError(SsoConnectorErrorCodes.InvalidConfig, {
+        config: this._idpConfig,
+        message: SsoConnectorConfigErrorCodes.InvalidConnectorConfig,
+      });
     }
 
     return this._idpConfig;
@@ -110,7 +117,11 @@ class SamlConnector {
     const rawProfileParseResult = userProfileGuard.safeParse(samlAssertionContent);
 
     if (!rawProfileParseResult.success) {
-      throw new ConnectorError(ConnectorErrorCodes.InvalidResponse, rawProfileParseResult.error);
+      throw new SsoConnectorError(SsoConnectorErrorCodes.AuthorizationFailed, {
+        message: 'Invalid SAML assertion',
+        response: samlAssertionContent,
+        error: rawProfileParseResult.error.flatten(),
+      });
     }
 
     const rawUserProfile = rawProfileParseResult.data;
@@ -149,7 +160,14 @@ class SamlConnector {
 
       return loginRequest.context;
     } catch (error: unknown) {
-      throw new ConnectorError(ConnectorErrorCodes.General, error);
+      if (error instanceof SsoConnectorError) {
+        throw error;
+      }
+
+      throw new SsoConnectorError(SsoConnectorErrorCodes.InvalidMetadata, {
+        message: SsoConnectorConfigErrorCodes.InvalidConnectorConfig,
+        error,
+      });
     }
   }
 
@@ -197,7 +215,11 @@ class SamlConnector {
     const result = samlIdentityProviderMetadataGuard.safeParse(this.idpConfig);
 
     if (!result.success) {
-      throw new ConnectorError(ConnectorErrorCodes.InvalidConfig, result.error);
+      throw new SsoConnectorError(SsoConnectorErrorCodes.InvalidConfig, {
+        config: this.idpConfig,
+        message: SsoConnectorConfigErrorCodes.InvalidConnectorConfig,
+        error: result.error.flatten(),
+      });
     }
 
     return result.data;
diff --git a/packages/core/src/sso/SamlConnector/utils.ts b/packages/core/src/sso/SamlConnector/utils.ts
index ec4fd60bc..a7dc49011 100644
--- a/packages/core/src/sso/SamlConnector/utils.ts
+++ b/packages/core/src/sso/SamlConnector/utils.ts
@@ -1,12 +1,16 @@
 import * as validator from '@authenio/samlify-node-xmllint';
-import { ConnectorError, ConnectorErrorCodes } from '@logto/connector-kit';
 import { type Optional, conditional, appendPath } from '@silverhand/essentials';
-import { got } from 'got';
+import { HTTPError, got } from 'got';
 import * as saml from 'samlify';
 import { z } from 'zod';
 
 import { ssoPath } from '#src/routes/interaction/const.js';
 
+import {
+  SsoConnectorConfigErrorCodes,
+  SsoConnectorError,
+  SsoConnectorErrorCodes,
+} from '../types/error.js';
 import {
   defaultAttributeMapping,
   type CustomizableAttributeMap,
@@ -56,7 +60,11 @@ export const parseXmlMetadata = (
   const result = samlIdentityProviderMetadataGuard.safeParse(rawSamlMetadata);
 
   if (!result.success) {
-    throw new ConnectorError(ConnectorErrorCodes.InvalidMetadata, result.error);
+    throw new SsoConnectorError(SsoConnectorErrorCodes.InvalidMetadata, {
+      message: SsoConnectorConfigErrorCodes.InvalidConnectorConfig,
+      metadata: rawSamlMetadata,
+      error: result.error,
+    });
   }
 
   return result.data;
@@ -75,13 +83,23 @@ export const fetchSamlMetadataXml = async (metadataUrl: string): Promise<Optiona
     const result = z.string().safeParse(body);
 
     if (!result.success) {
-      throw new ConnectorError(ConnectorErrorCodes.InvalidConfig, result.error);
+      throw new SsoConnectorError(SsoConnectorErrorCodes.InvalidMetadata, {
+        message: SsoConnectorConfigErrorCodes.InvalidConfigResponse,
+        metadata: body,
+        error: result.error,
+      });
     }
 
     return result.data;
   } catch (error: unknown) {
-    // HTTP request error
-    throw new ConnectorError(ConnectorErrorCodes.General, error);
+    if (error instanceof SsoConnectorError) {
+      throw error;
+    }
+
+    throw new SsoConnectorError(SsoConnectorErrorCodes.InvalidMetadata, {
+      message: SsoConnectorConfigErrorCodes.FailToFetchConfig,
+      error: error instanceof HTTPError ? error.response.body : error,
+    });
   }
 };
 
@@ -107,7 +125,11 @@ export const getExtendedUserInfoFromRawUserProfile = (
   const result = extendedSocialUserInfoGuard.safeParse(mappedUserProfile);
 
   if (!result.success) {
-    throw new ConnectorError(ConnectorErrorCodes.InvalidResponse, result.error);
+    throw new SsoConnectorError(SsoConnectorErrorCodes.AuthorizationFailed, {
+      message: 'Invalid SAML assertion',
+      response: mappedUserProfile,
+      error: result.error.flatten(),
+    });
   }
 
   return result.data;
@@ -152,7 +174,10 @@ export const handleSamlAssertion = async (
       ...assertionResult.extract.attributes,
     };
   } catch (error: unknown) {
-    throw new ConnectorError(ConnectorErrorCodes.General, String(error));
+    throw new SsoConnectorError(SsoConnectorErrorCodes.AuthorizationFailed, {
+      message: 'Invalid SAML assertion',
+      error,
+    });
   }
 };
 
diff --git a/packages/core/src/sso/SamlSsoConnector/index.test.ts b/packages/core/src/sso/SamlSsoConnector/index.test.ts
index 7a92e26b9..9fd9bf240 100644
--- a/packages/core/src/sso/SamlSsoConnector/index.test.ts
+++ b/packages/core/src/sso/SamlSsoConnector/index.test.ts
@@ -1,8 +1,12 @@
-import { ConnectorError, ConnectorErrorCodes } from '@logto/connector-kit';
 import { SsoProviderName } from '@logto/schemas';
 
 import { mockSsoConnector as _mockSsoConnector } from '#src/__mocks__/sso.js';
 
+import {
+  SsoConnectorConfigErrorCodes,
+  SsoConnectorError,
+  SsoConnectorErrorCodes,
+} from '../types/error.js';
 import { type SamlConnectorConfig } from '../types/saml.js';
 
 import { samlSsoConnectorFactory } from './index.js';
@@ -35,7 +39,10 @@ describe('SamlSsoConnector', () => {
     const connector = new samlSsoConnectorFactory.constructor(mockSsoConnector, 'default_tenant');
 
     await expect(async () => connector.getSamlIdpMetadata()).rejects.toThrow(
-      new ConnectorError(ConnectorErrorCodes.InvalidConfig, 'config not found')
+      new SsoConnectorError(SsoConnectorErrorCodes.InvalidConfig, {
+        config: undefined,
+        message: SsoConnectorConfigErrorCodes.InvalidConnectorConfig,
+      })
     );
   });
 
diff --git a/packages/core/src/sso/SamlSsoConnector/index.ts b/packages/core/src/sso/SamlSsoConnector/index.ts
index 44001b4dd..ba238d84d 100644
--- a/packages/core/src/sso/SamlSsoConnector/index.ts
+++ b/packages/core/src/sso/SamlSsoConnector/index.ts
@@ -1,11 +1,12 @@
-import { type SsoConnector, SsoProviderName } from '@logto/schemas';
+import { SsoProviderName } from '@logto/schemas';
 import { conditional, trySafe } from '@silverhand/essentials';
 
+import RequestError from '#src/errors/RequestError/index.js';
 import assertThat from '#src/utils/assert-that.js';
 
 import SamlConnector from '../SamlConnector/index.js';
 import { type SingleSignOnFactory } from '../index.js';
-import { type SingleSignOn } from '../types/index.js';
+import { type SingleSignOn, type SingleSignOnConnectorData } from '../types/index.js';
 import { samlConnectorConfigGuard, type SamlMetadata } from '../types/saml.js';
 import {
   type SingleSignOnConnectorSession,
@@ -26,7 +27,7 @@ import {
  */
 export class SamlSsoConnector extends SamlConnector implements SingleSignOn {
   constructor(
-    readonly data: SsoConnector,
+    readonly data: SingleSignOnConnectorData,
     tenantId: string
   ) {
     const parseConfigResult = samlConnectorConfigGuard.safeParse(data.config);
@@ -90,7 +91,7 @@ export class SamlSsoConnector extends SamlConnector implements SingleSignOn {
    * This method only asserts the userInfo is not null and directly return it.
    */
   async getUserInfo({ userInfo }: SingleSignOnConnectorSession) {
-    assertThat(userInfo, 'session.connector_validation_session_not_found');
+    assertThat(userInfo, new RequestError('session.connector_session_not_found'));
 
     return userInfo;
   }
diff --git a/packages/core/src/sso/index.ts b/packages/core/src/sso/index.ts
index 1cf4af7c7..d39b7c5ee 100644
--- a/packages/core/src/sso/index.ts
+++ b/packages/core/src/sso/index.ts
@@ -24,7 +24,7 @@ type SingleSignOnConstructor = {
   [SsoProviderName.OKTA]: typeof OktaSsoConnector;
 };
 
-type SingleSignOnConnectorConfig = {
+export type SingleSignOnConnectorConfig = {
   [SsoProviderName.OIDC]: typeof basicOidcConnectorConfigGuard;
   [SsoProviderName.SAML]: typeof samlConnectorConfigGuard;
   [SsoProviderName.AZURE_AD]: typeof samlConnectorConfigGuard;
diff --git a/packages/core/src/sso/types/error.ts b/packages/core/src/sso/types/error.ts
new file mode 100644
index 000000000..7c293b97b
--- /dev/null
+++ b/packages/core/src/sso/types/error.ts
@@ -0,0 +1,66 @@
+import { ConnectorError, ConnectorErrorCodes } from '@logto/connector-kit';
+import { type JsonObject } from '@logto/schemas';
+
+export enum SsoConnectorErrorCodes {
+  InvalidMetadata = 'invalid_metadata',
+  InvalidConfig = 'invalid_config',
+  AuthorizationFailed = 'authorization_failed',
+  InvalidResponse = 'invalid_response',
+  InvalidRequestParameters = 'invalid_request_parameters',
+}
+
+export enum SsoConnectorConfigErrorCodes {
+  InvalidConfigResponse = 'invalid_config_response',
+  FailToFetchConfig = 'fail_to_fetch_config',
+  InvalidConnectorConfig = 'invalid_connector_config',
+}
+
+const connectorErrorCodeMap: { [key in SsoConnectorErrorCodes]: ConnectorErrorCodes } = {
+  [SsoConnectorErrorCodes.InvalidMetadata]: ConnectorErrorCodes.InvalidMetadata,
+  [SsoConnectorErrorCodes.InvalidConfig]: ConnectorErrorCodes.InvalidConfig,
+  [SsoConnectorErrorCodes.InvalidResponse]: ConnectorErrorCodes.InvalidResponse,
+  [SsoConnectorErrorCodes.InvalidRequestParameters]: ConnectorErrorCodes.InvalidRequestParameters,
+  [SsoConnectorErrorCodes.AuthorizationFailed]: ConnectorErrorCodes.AuthorizationFailed,
+};
+
+export class SsoConnectorError extends ConnectorError {
+  constructor(
+    code: SsoConnectorErrorCodes.InvalidMetadata,
+    data: { message: SsoConnectorConfigErrorCodes; metadata?: string | JsonObject; error?: unknown }
+  );
+
+  constructor(
+    code: SsoConnectorErrorCodes.InvalidConfig,
+    data: {
+      message: SsoConnectorConfigErrorCodes;
+      config: JsonObject | undefined;
+      error?: unknown;
+    }
+  );
+
+  constructor(
+    code: SsoConnectorErrorCodes.InvalidRequestParameters,
+    data: { url: string; params: unknown; error?: unknown }
+  );
+
+  constructor(
+    code: SsoConnectorErrorCodes.InvalidResponse,
+    data: {
+      url: string;
+      response: unknown;
+      error?: unknown;
+    }
+  );
+
+  constructor(
+    code: SsoConnectorErrorCodes.AuthorizationFailed,
+    data: { message: string; response?: unknown; error?: unknown }
+  );
+
+  constructor(code: SsoConnectorErrorCodes, data?: Record<string, unknown>) {
+    super(connectorErrorCodeMap[code], {
+      ssoErrorCode: code,
+      ...data,
+    });
+  }
+}
diff --git a/packages/core/src/sso/types/index.ts b/packages/core/src/sso/types/index.ts
index e9db2c88c..50684b1b0 100644
--- a/packages/core/src/sso/types/index.ts
+++ b/packages/core/src/sso/types/index.ts
@@ -1,4 +1,4 @@
-import { type JsonObject, type SsoConnector } from '@logto/schemas';
+import { type SsoProviderName, type JsonObject, type SsoConnector } from '@logto/schemas';
 
 export * from './session.js';
 
@@ -10,7 +10,13 @@ export * from './session.js';
  * @method {getConfig} getConfig - Get the full-list of SSO config from the SSO provider
  */
 export abstract class SingleSignOn {
-  abstract data: SsoConnector;
+  abstract data: SingleSignOnConnectorData;
   abstract getConfig: () => Promise<JsonObject>;
   abstract getIssuer: () => Promise<string>;
 }
+
+// Pick the required fields from SsoConnector Schema
+// providerName must be supported by the SSO connector factories
+export type SingleSignOnConnectorData = Pick<SsoConnector, 'config' | 'id'> & {
+  providerName: SsoProviderName;
+};
diff --git a/packages/integration-tests/src/tests/api/interaction/single-sign-on/sad-path.test.ts b/packages/integration-tests/src/tests/api/interaction/single-sign-on/sad-path.test.ts
index 9d25588d5..b0acc703b 100644
--- a/packages/integration-tests/src/tests/api/interaction/single-sign-on/sad-path.test.ts
+++ b/packages/integration-tests/src/tests/api/interaction/single-sign-on/sad-path.test.ts
@@ -102,8 +102,8 @@ describe('Single Sign On Sad Path', () => {
       await expectRejects(
         postSamlAssertion({ connectorId, RelayState, SAMLResponse: samlAssertion }),
         {
-          code: 'connector.general',
-          statusCode: 400,
+          code: 'connector.authorization_failed',
+          statusCode: 401,
         }
       );
     });