Well, considering Naruto's journey and growth, Minato, his son in the fanfiction, could have some sort of emotional - power - based ability. For example, he could have the ability to draw strength from the bonds he forms with others, just like Naruto does. And since Naruto has befriended so many different people from various clans and villages, Minato might have an ability that is enhanced by the diverse relationships he has access to. Maybe he can even use this to create a sort of group - based chakra boost for himself and his allies during battles.
He could inherit Naruto's chakra - rich nature. So, he might have a large reserve of chakra like his father. Also, since Naruto has the Nine - Tails' chakra, Minato might have some sort of unique connection to it as well, perhaps being able to access a small portion of its power in a different way than Naruto does. And of course, he could inherit some of Naruto's signature jutsu like the Rasengan, but with his own twist.