If his dad's name on his birth certificate, are you sure he can't have British nationality?
As far as I am aware, he can.
My DGS was not born in the UK but has a British passport through DD who was born here.
His father is not British.
If they came to live here, his father would probably not be able to stay because the country where he was born is not a member of the EU.
It is a Commonwealth country and they have been abandoned in favour of the EU, so spouses of British citizens who were born in Commonwealth countries are being deported.
The scenario you describe, Djen, may never happen, and if we did leave the EU then I am sure people already living here legally would not be deported.