I know someone with at least three citizenships. Born in waters off Australia, to one Greek and one New Zealander parent, so has citizenship in three countries! Not automatic, though,; parents had to apply in all three countries. If they hadn't, I wonder whether he would have been a non-citizen!
Some one born in International waters has some kinds of choice about citizenship, I think.
Not sure about someone born in airspace above a country, though.
Cheers
Mick