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.
In this fanfiction, Naruto might take the baby in and raise it as his own. He could teach the baby ninjutsu skills he has learned over the years. Maybe the baby has some special powers that are gradually discovered as the story progresses.
The baby could turn out to have some sort of special chakra. Naruto, being curious and always wanting to help, tries to find out more about it. He might seek help from Kakashi or other experienced ninjas.
Well, Naruto might try to protect the baby dragon from any harm. He could use his ninja skills to keep it safe from enemies who might want to capture it for its power or rarity.
Well, Naruto might take the baby wolf to his home in the village. He could raise it as his own, teaching it ninja skills when it grows up. Maybe the wolf would become his loyal companion, like how Akamaru is to Kiba.
Another way the story could go is that the baby has a unique ability that attracts the attention of other villages. Naruto then has to protect the baby from those who might want to use its power for bad. He could train the baby to control its power and also form alliances with other villages to ensure the baby's safety. Along the way, the baby could learn about Naruto's own past and be inspired to become a strong and kind ninja like him.
There's a fanfiction called 'Tsunade and the Infant Naruto'. Here, Tsunade's discovery of baby Naruto leads to a series of events that change the course of Naruto's early life. Tsunade starts to secretly train Naruto in her own special techniques, away from the prying eyes of the village. This gives Naruto an edge later on when he starts his official ninja training. The fanfiction also delves into how Tsunade's presence affects Naruto's self - esteem and his view of the world around him.
You can try fanfiction websites like FanFiction.net or Archive of Our Own. Just search for 'Kakashi finds baby Naruto' on their search bars, and you'll likely find some relevant fanfictions.
Well, Naruto finding a baby boy in a fanfiction could lead to all sorts of adventures. Maybe the baby has some special power or is a key to some mystery in the Naruto world. Naruto would then have to protect the baby from those who would want to use the baby's power for evil.
He could decide to protect the baby girl himself. Naruto has a big heart. He might see the baby as someone he needs to look after, just like how he was always looking out for his friends. Maybe he starts teaching her some basic ninja skills when she grows a bit older.