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By following these below steps, this should help you to diagnose and resolve the 404 errors related to your .svc files in Azure App Service.
- Confirm that all of the app's files and folders are deployed by comparing the deployment on the hosting system to the contents of the project's publish folder. For more information on the layout of a published ASP.NET Core app, see ASP.NET Core directory structure.
- The error is usually caused by a broken deployment on the hosting system, which includes scenarios such as the app being deployed to the wrong folder or the web.config file being missing or malformed. Perform the following steps: Delete all of the files and folders from the deployment folder on the hosting system and redeploy the contents of the app's publish folder. Confirm that the web.config file is present in the deployment and that its contents are correct.
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Deepanshu