I'm not sure who Shiro's father is in this specific 'Naruto' fanfiction as there could be many different interpretations created by various fanfic authors.
In some fanfictions, Minato could be Naruto's father in the context of the Kyuubi. Since Minato was Naruto's actual father in the original series and the Kyuubi was sealed within Naruto by Minato. So many fanfictions might expand on their relationship within the framework of the Kyuubi's presence.
In fanfiction, Naruto could be portrayed in various ways. He might be a character with new relationships and roles. Without reading the specific 'naruto father of yasaka fanfiction', it's hard to say exactly. But generally, he could be a father figure to Yasaka, which would likely involve a lot of character development and new storylines related to protecting, guiding, or having a special bond with Yasaka.
Well, if Naruto is the father of Mikoto in the fanfiction, it could bring a whole new dynamic. Naruto is known for his strong will and his ability to make friends and change people's minds. As Mikoto's father, he might instill in her the same values. Also, considering Naruto's connection to the Nine - Tails, there could be some interesting plot twists. For example, Mikoto might have some sort of special ability related to the Nine - Tails or Naruto could have passed on some of his chakra to her, which would give her an edge in battles.
Well, it could be anyone really. It might be some random ninja that Rouge had a relationship with. Or it could be a character created specifically for this fanfiction. Maybe it could even be a character from another village who had a secret liaison with Rouge.
It could be Sasuke. Their relationship has always been complex in the original Naruto story. In the fanfiction, their relationship might have developed into a romantic one, leading to the birth of the child. The child would then inherit traits from both of them, perhaps Sasuke's cool-headedness and Fem Naruto's determination.
It could be an ancient sage. In Naruto lore, there are sages who have had a great influence on the world. An ancient sage could be the one who created or fathered the bijuu. Maybe he had some great power and knowledge that allowed him to bring the bijuu into existence.
In fanfiction, the possibilities for Naruto's father could be many. It could be an original character created by the author. Maybe a powerful shinobi who has a connection with the female Shinigami. For example, he could be a shinobi who made a deal with the Shinigami in the past and through some convoluted plot, became Naruto's father.
It could be someone from the other universe in the crossover. For example, if it's a crossover with a superhero universe, it could be a character like Superman. The combination of Naruto's strong ninja genes and Superman's superpowers would make for an extremely powerful child. Or it could be a character from a high - fantasy world, like a powerful mage. Their union would bring about a child with a mix of magic and ninja abilities.