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.
It could be Hinata. Since they are in a relationship in the original series, it would be a natural choice. Hinata would be a loving and caring mother, and her gentle nature would be a great influence on the baby.
In a fanfiction world where Naruto and Rin have a baby, it could be a very interesting story. Maybe the baby would inherit Naruto's positive attitude and Rin's kindness. The story could explore how they raise the child in a world full of challenges and ninjas.
One idea could be that the baby is from a hidden clan. Naruto decides to protect the baby from those who would use its special abilities. He takes the baby under his wing and trains it as it grows up, passing on his ninja values.
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.
Naruto uses his ninja skills. He's always on high alert, using his enhanced senses to detect any potential danger. His quick reflexes mean he can react in an instant if anything threatens the baby.
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 interesting scenario could be baby Sasuke and baby Naruto getting into innocent mischief together in the Hidden Leaf Village. Maybe they accidentally let all the chickens loose in the market area while playing a game of chase.
It could be a completely new character. Maybe Naruto met her during his travels, and for some reason, she had to entrust the baby to Naruto. This could be due to her being in danger or having some kind of mission that made it impossible for her to take care of the baby herself.
Perhaps the baby could be named Kazuki. It gives a sense of being strong and noble, which would be fitting for the child of Naruto and Hinata. In fanfiction, the name could also be symbolic of a new beginning or a special power that the baby might possess, like being related to the combination of Naruto's Nine - Tailed Fox power and Hinata's Byakugan abilities.