diff --git a/packages/core/src/libraries/jwt-customizer.ts b/packages/core/src/libraries/jwt-customizer.ts
index b48563a70..798f5b8bd 100644
--- a/packages/core/src/libraries/jwt-customizer.ts
+++ b/packages/core/src/libraries/jwt-customizer.ts
@@ -1,4 +1,3 @@
-import { buildErrorResponse, runScriptFunctionInLocalVm } from '@logto/core-kit/custom-jwt';
 import {
   LogtoJwtTokenKeyType,
   jwtCustomizerUserContextGuard,
@@ -22,6 +21,8 @@ import type Queries from '#src/tenants/Queries.js';
 import {
   LocalVmError,
   getJwtCustomizerScripts,
+  runScriptFunctionInLocalVm,
+  buildLocalVmErrorBody,
   type CustomJwtDeployRequestBody,
 } from '#src/utils/custom-jwt/index.js';
 
@@ -53,7 +54,7 @@ export class JwtCustomizerLibrary {
       }
 
       throw new LocalVmError(
-        buildErrorResponse(error),
+        buildLocalVmErrorBody(error),
         error instanceof SyntaxError || error instanceof TypeError ? 422 : 500
       );
     }
diff --git a/packages/core/src/utils/custom-jwt/custom-jwt.ts b/packages/core/src/utils/custom-jwt/custom-jwt.ts
deleted file mode 100644
index d7f194db8..000000000
--- a/packages/core/src/utils/custom-jwt/custom-jwt.ts
+++ /dev/null
@@ -1,10 +0,0 @@
-import { LogtoJwtTokenKey, type JwtCustomizerType } from '@logto/schemas';
-
-import { type CustomJwtDeployRequestBody } from './types.js';
-
-export const getJwtCustomizerScripts = (jwtCustomizers: Partial<JwtCustomizerType>) => {
-  // eslint-disable-next-line no-restricted-syntax -- enable to infer the type using `Object.fromEntries`
-  return Object.fromEntries(
-    Object.values(LogtoJwtTokenKey).map((key) => [key, { production: jwtCustomizers[key]?.script }])
-  ) as CustomJwtDeployRequestBody;
-};
diff --git a/packages/core/src/utils/custom-jwt/index.ts b/packages/core/src/utils/custom-jwt/index.ts
index bdaa0d30d..5a60eacb4 100644
--- a/packages/core/src/utils/custom-jwt/index.ts
+++ b/packages/core/src/utils/custom-jwt/index.ts
@@ -1,3 +1,13 @@
-export * from './custom-jwt.js';
+import { LogtoJwtTokenKey, type JwtCustomizerType } from '@logto/schemas';
+
+import { type CustomJwtDeployRequestBody } from './types.js';
+
 export * from './types.js';
-export * from './local-vm-error.js';
+export * from './local-vm.js';
+
+export const getJwtCustomizerScripts = (jwtCustomizers: Partial<JwtCustomizerType>) => {
+  // eslint-disable-next-line no-restricted-syntax -- enable to infer the type using `Object.fromEntries`
+  return Object.fromEntries(
+    Object.values(LogtoJwtTokenKey).map((key) => [key, { production: jwtCustomizers[key]?.script }])
+  ) as CustomJwtDeployRequestBody;
+};
diff --git a/packages/core/src/utils/custom-jwt/local-vm-error.ts b/packages/core/src/utils/custom-jwt/local-vm-error.ts
deleted file mode 100644
index 64d250fad..000000000
--- a/packages/core/src/utils/custom-jwt/local-vm-error.ts
+++ /dev/null
@@ -1,17 +0,0 @@
-import { ResponseError } from '@withtyped/client';
-
-// Extend the ResponseError from @withtyped/client, so that we can unify the error handling and display logic for both OSS version and Cloud version.
-export class LocalVmError extends ResponseError {
-  constructor(errorBody: Record<string, unknown>, statusCode: number) {
-    super(
-      new Response(
-        new Blob([JSON.stringify(errorBody)], {
-          type: 'application/json',
-        }),
-        {
-          status: statusCode,
-        }
-      )
-    );
-  }
-}
diff --git a/packages/toolkit/core-kit/src/custom-jwt/script-execution.ts b/packages/core/src/utils/custom-jwt/local-vm.ts
similarity index 54%
rename from packages/toolkit/core-kit/src/custom-jwt/script-execution.ts
rename to packages/core/src/utils/custom-jwt/local-vm.ts
index 32ee65f4c..aa4c08fd2 100644
--- a/packages/toolkit/core-kit/src/custom-jwt/script-execution.ts
+++ b/packages/core/src/utils/custom-jwt/local-vm.ts
@@ -1,5 +1,28 @@
+import { types } from 'node:util';
 import { runInNewContext } from 'node:vm';
 
+import { ResponseError } from '@withtyped/client';
+
+/**
+ * Extend the ResponseError from @withtyped/client.
+ * This class is used to parse the error from the local VM to the WithTyped client response error.
+ * So we can unify the error handling and display logic for both local VM and Cloud version.
+ */
+export class LocalVmError extends ResponseError {
+  constructor(errorBody: Record<string, unknown>, statusCode: number) {
+    super(
+      new Response(
+        new Blob([JSON.stringify(errorBody)], {
+          type: 'application/json',
+        }),
+        {
+          status: statusCode,
+        }
+      )
+    );
+  }
+}
+
 /**
  * This function is used to execute a named function in a customized code script in a local
  * virtual machine with the given payload as input.
@@ -39,3 +62,18 @@ export const runScriptFunctionInLocalVm = async (
 
   return result;
 };
+
+/**
+ * Build the error body for the local VM error.
+ *
+ * @remarks
+ *
+ * Catch the error from vm module, and build the error body.
+ * Use `isNativeError` to check if the error is an instance of `Error`.
+ * If the error comes from `node:vm` module, then it will not be an instance of `Error` but can be captured by `isNativeError`.
+ *
+ */
+export const buildLocalVmErrorBody = (error: unknown) =>
+  types.isNativeError(error)
+    ? { message: error.message, stack: error.stack }
+    : { message: String(error) };
diff --git a/packages/toolkit/core-kit/src/custom-jwt/error-handling.ts b/packages/toolkit/core-kit/src/custom-jwt/error-handling.ts
deleted file mode 100644
index ae013172b..000000000
--- a/packages/toolkit/core-kit/src/custom-jwt/error-handling.ts
+++ /dev/null
@@ -1,10 +0,0 @@
-import { types } from 'node:util';
-
-export const buildErrorResponse = (error: unknown) =>
-  /**
-   * Use `isNativeError` to check if the error is an instance of `Error`.
-   * If the error comes from `node:vm` module, then it will not be an instance of `Error` but can be captured by `isNativeError`.
-   */
-  types.isNativeError(error)
-    ? { message: error.message, stack: error.stack }
-    : { message: String(error) };
diff --git a/packages/toolkit/core-kit/src/custom-jwt/index.ts b/packages/toolkit/core-kit/src/custom-jwt/index.ts
deleted file mode 100644
index 5d732ce66..000000000
--- a/packages/toolkit/core-kit/src/custom-jwt/index.ts
+++ /dev/null
@@ -1,2 +0,0 @@
-export * from './script-execution.js';
-export * from './error-handling.js';