Api Creation

As Sam said, API is not a Web application. You use ASP.NET to build Web applications. API usually is a DLL and created using a language such as C# and it does not have a user interface. ASP.NET is used to create user interfaces.

The term Application Programming Interface (API) is not clearly defined but typically it is a set of functions existing in one or more regular DLLs that is called from unmanaged code. It is difficult or impossible to write that in a managed language such as C#. So unless you can provide clarification, the answer is that it cannot be done using C#.
 
Note that ASP .Net is an environment, not a language.
 

i need to create the my web application as a api.