Probably the only solution that you can create ASP.NET projects on Linux is MonoDevelop. How to install the software can be found here. Xamarin Studio was a much better solution, but it is no longer developed. The last version is 6.4. Now Xamarin is included in Visual Studio.
MonoDevelop enables developers to quickly write desktop and web
applications on Linux, Windows and Mac OS. It also makes it easy for
developers to port .NET applications created with Visual Studio to
Linux and Mac OS maintaining a single code base for all platforms.
MonoDevelop is now a part of Microsoft Xamarin Studio.
JetBrains offers a variety of tools to create .Net Technologies apps. You can find all product on the official webpage. For exmample JetBrains Rider supports .NET Framework, the new cross-platform .NET Core, and Mono based projects. This lets you develop a wide array of applications including .NET desktop applications, services and libraries, Unity games, Xamarin apps, ASP.NET and ASP.NET Core web applications.