Accepted answer

Use Bootstrap

Bootstrap is the most popular HTML, CSS, and JS framework for developing responsive, mobile first projects on the web.

Okay thanks

Creating an ASP.NET Mobile Web Application

https://msdn.microsoft.com/en-us/library/aa671837(v=vs.71).aspx

I think there is nothing like "a mobile asp.net c# website"

Either you can build an android app or a Xamarian app in Visual Studio.

Or you can build an ASP.Net website with controls which are adjusted as per mobile device.

Asp.net c# mobile website