How to implement a two-factor authentication web service?

Question

ASP.NET

Good afternoon. There is a task to implement a two-factor authentication web service. It is expected that other websites will be able to use this service to authenticate their users. In my understanding, you need to write something similar to Google or vk.com authentication, but I have no idea how to write it. Those. in the end, you should get two separately working applications, one of which accesses the other through requests (or can use the contents of the page of the other).
Authentication itself has already been done (sms, email, webcam and qr-code).

Answer 1

OAuth ?
OAuth provides client applications a 'secure delegated access' to server resources on behalf of a resource owner.

Answer 2

as Deerenaros already said , you need to accept an authorization request from a web application to your service, then the service performs checks (what you will have there) and if it thinks that everything is OK, it sends a response to the web application that sent the request.