I think you're mixing two different technologies.
A REST endpoint belongs to WebServices and is an url, pointing to one or more methods in your code that can accept parameters and return results in XML/JSON format.
You can then fetch this url from your front-end and read the response.
An example of REST webservice is Google Maps API.
A Websocket, instead, is a continuous connection and works as a plain socket but between a webpage running on a client and another server application on another machine (i.e. the server).
It's used when you need an open tunnel with continuous exchange of data: chats, video and audio streaming, multiplayer games and more.
You cannot make a REST call to a websocket endpoint and if you want to use websockets you must write a server in C# (i use .net core). A console application.
I'm unsure what you are looking for exactly. If you want to start with websockets, this is where i started from:
Writing websocket server
Writing a websocket server in C#
For webservices:
Writing a web service in ASP.NET