How to authorizing from asp Mvc site & API

Question

I have asp MVC project with API ,Now I Want make Startup.Auth.cs to authentcation access from site and API 

 

1- This is my Startup.Auth.cs that work with site

 

 

 

 

2- And this Startup.Auth.cs that work with api

 

 

 

 

How Can make Startup.Auth.cs that can works with site and API ?