Well, he might have shown superhuman strength, like being able to break things that normal babies couldn't. Maybe he could also sense danger in an uncanny way, like a sixth sense.
It could make Naruto more responsible. Since he has to take care of the baby fox, he'll have to think about another being's needs. For example, he can't just go on long missions without making arrangements for the fox.
Well, one possible plot could be that the baby fox has some special powers. Maybe it can communicate with Naruto telepathically and helps him in his ninja missions. For example, it could sense danger before Naruto does and warn him.
The baby sister could change Naruto in some ways. He might become more responsible and less reckless. He would have to think about her well - being all the time. For example, he might not take on as many dangerous missions so that he can be around to protect her. And as she grows up, she could also inspire Naruto to strive for a better future for the Hidden Leaf Village, not just for himself but for her as well.
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.