The correct answer is "meines Vater". Why's that?
Uses of the German Genitive Case!
Although genitive isn’t common any more, it’s still used in several, important contexts.
1. Possession This is the most common and well-known use of the genitive, the equivalent to “this is the ____ of my aunt.”
How do you use German genitive case to show possession? To show possession with the German genitive case, start with the object that’s being possessed. Say it’s a gift, das Geschenk. Then figure out who’s doing the possessing. Say it’s your boyfriend you’re talking about, mein Freund (my boyfriend). So you would want to say the equivalent of “The gift of my boyfriend,” which is:
Das Geschenk meines Freunds.
Examples: Das Haar der Frau. (The woman’s hair.) Das Auto der Eltern meiner Freundin. (The car of the parents of my girlfriend.) Die Tasche seiner Mutter. (The bag of his mother.)
Note: The possessive in German can also be expressed with an s the way it is in English, but beware: Don’t use an apostrophe the way you do in English. Some Germans have started using an apostrophe, but it’s considered poor form.
So you would say Marias Auto (Maria’s car), not Maria’s Auto.