Custom authentication system look like Facebook.

Could someone tell me how to implement this solution?

Problem description: We have an "A" system that stores user data. There is also a whole network of systems B, C, D where I would like to implement the "Login through" button to log on to one of the accounts on the system A. (Mechanism as this Facebook, however, with its own authorization server).

I would like to do this in Symfony3.

Any suggestions on how to create such a mechanism? How to play on the content?

On the web I came across the information that this allows oAuth2, but how to get the desired effect? Maybe someone met a similar problem?

Regards, Rafał Malik