Hello Boyan Stefanov,
Welcome to the Microsoft Q&A and thank you for posting your questions here.
I understand that you are having challenges to perform authentication in container apps through Front Door's custom domain.
To configure authentication and authorization for your Azure Container App with Front Door and Microsoft Entra ID, you will need to create an App Registration Automatically. From Azure portal you will navigate to your app and select Authentication, to add Identity Provider by selecting Microsoft as the identity provider. By default, the option to create a new registration is selected. You can customize the registration name and supported account types and configure your client secret to generate and store as a secret in the container app. https://learn.microsoft.com/en-us/azure/container-apps/authentication-entra
Also, if you like you can configure it manually.
You can check a similar answer here if you use a private link https://learn.microsoft.com/en-us/answers/questions/1689342/front-door-with-azure-container-apps-and-private-l
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I hope this is helpful! Do not hesitate to let me know if you have any other questions.
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Best Regards,
Sina Salam