Call FB api inside my site api

Could probably not pinning down the right term that's why I'm not getting any result, and I guess I'm not just the one. My search and google skills are exhausted and I could no longer spare time doing the search, (sorry, to show some impatience).

Anyway, I have created an API-centric website, together with a mobile application and I am planning consuming FB api say for eg. the login api calls but then I want to use/re-use the API I've developed, is it possible to call another api (fb api for eg) and process the return via my custom made api?

I can't find any examples, I presume again I'm not the only one looking for this, so there must be resources available out there, can someone help me find that?

Thanks in advance.