One possible character could be Jiraiya. He was Naruto's mentor later in life, but in a fanfiction, he could have taken Naruto as a baby. He had a close relationship with Naruto's father, so it would make sense for him to take Naruto under his wing from the start. Another could be Tsunade. As one of the Sannin, she has the power and the means to protect Naruto. Plus, she might have seen it as her duty to take care of the son of her old teammate.
Kushina would take care of baby Naruto very tenderly. She would make sure he is well - fed before sleep, perhaps by breastfeeding him or giving him a warm bottle. She'd also check his diaper and change it if needed.
His friends like Sakura and Sasuke might step in to take care of him. Sakura, with her nurturing side, could handle feeding and cleaning him. Sasuke, though he might seem reluctant at first, would probably also protect the baby Naruto from any threats.
Well, it's mainly baby Sasuke and baby Naruto. But sometimes other characters from the Naruto universe might make an appearance in the fanfiction. For instance, Iruka Sensei could be the one looking after them, or Sakura as a baby might be in the background. However, the spotlight is mostly on baby Sasuke and baby Naruto as they are the ones around which the whole concept of this fanfiction revolves.
One character that might be in 'Naruto' baby daddy fanfics is Karin. She has had interactions with Naruto in the series. Although their relationship was not of a romantic nature in the original, fanfic writers can take creative liberties. They can create a story where Karin and Naruto have a relationship that leads to a baby. Also, there could be original characters created just for the fanfic that become the mother or have some other important role in the story about Naruto being a baby daddy.
Family. It could focus on how Naruto and Kurenai form a new family with the baby. They learn about parenting, love, and sacrifice.
One possible plotline could be Naruto's first attempts at using chakra as a baby. It would be really cute to see him unknowingly channel his chakra while playing with a toy, and then get a big surprised look on his face when something unexpected happens.
In Naruto fanfiction, characters like Jiraiya could also be a 'baby daddy'. He was known for his womanizing ways in the series, so it's not hard to fathom a situation where he has a child. Then there's Itachi. Although his life was full of tragedy and secrecy, a fanfiction could explore a scenario where he has a child before his untimely death. And Kiba could be a character as well. His close bond with his dog Akamaru and his brash personality could lead to a situation where he becomes a 'baby daddy' in a creative fanfiction.
One idea could be that Naruto is taken by a powerful but reclusive ninja who trains him in secret from a young age. This way, Naruto grows up with a different set of skills and a more focused mindset, perhaps even learning some ancient and forgotten jutsu. Another plot could involve Naruto being taken by a group of kind-hearted villagers from another village. They raise him as their own, and he grows up with a different view of the world outside of Konoha, which could lead to some interesting interactions when he eventually returns to Konoha.
Sasuke would be suspicious at first. He's not one to trust easily. But once he realizes it's Naruto, he might see it as an opportunity to gain some new knowledge or power. He could also be a bit envious that Naruto has this time - traveling ability, thinking it gives Naruto an even greater advantage.
In this fanfiction, it could be that Naruto's death as a baby is the result of a conspiracy. Maybe some anti - Uzumaki or anti - Jinchuriki group within Konoha planned his death. This would then lead to a series of events where the truth is slowly uncovered by some of the more perceptive characters in the village. This could create a lot of internal conflict as characters have to choose between loyalty to the village and uncovering the truth about Naruto's death.