Kakashi would approach Naruto's pranks with a mix of discipline and love. For instance, if Naruto tries to scribble on the walls, Kakashi would stop him gently. He'd then sit Naruto down and show him where he can draw instead, like on a piece of paper. He'd also tell Naruto stories about how important it is to respect their home. When Naruto does something really naughty, like trying to pull the cat's tail, Kakashi would firmly say 'No' but then immediately follow it up with a hug. He wants Naruto to learn right from wrong but also wants to make sure Naruto knows he is loved no matter what.
Kakashi would become more nurturing. In the original, he was a teacher, but as an adoptive father, he'd have to be more affectionate. He might show his face more often to Naruto, as a sign of trust, and be more open about his emotions.
The appeal lies in the fact that it gives a chance to rewrite Naruto's early life in a way. In these fanfictions, Kakashi can be the positive influence that Naruto really needed at that young age. It also allows for exploring different character traits of Kakashi, like his paternal side which we don't see much in the original series.
A popular Kakashi and baby Naruto fanfic is about Kakashi accidentally time - travels back to when Naruto was a baby. He uses his knowledge of the future to try and make Naruto's life better from the start. He trains Naruto in secret, helps him with his chakra control, and also makes sure Naruto has a stable emotional support system, which in turn has a huge impact on Naruto's growth.
You can try fanfic websites like FanFiction.net. They usually have a large collection of fan - made stories, and there's a good chance you'll find some 'baby Kakashi fanfic' there.
Well, perhaps in the fanfiction, Sakura discovers she has a baby from some sort of mysterious experiment gone wrong. Kakashi, being the reliable and kind - hearted ninja he is, steps in to help her. He teaches her how to be a strong mother while also protecting the baby from those who might want to use it for their own evil purposes. They end up forming a little family unit of sorts.
Their relationship might develop with Minato becoming a mentor to baby Kakashi. He could start by teaching him simple things like how to hold a kunai properly.
One great 'baby Kakashi fanfic' could be the one where it focuses on his early training days as a baby ninja in training. It might show how he overcomes the initial difficulties in learning basic jutsu.
It could be Orochimaru. He might be interested in the baby for some dark experiment, thinking the baby has unique chakra or abilities that he can use for his own gain. He would stop at nothing to get his hands on the baby, which would put Kakashi and Sakura in a tough situation to protect it.
One popular story could be 'Kakashi's Unexpected Fatherhood' where Kakashi discovers he's a father in a very unexpected situation. Maybe a former lover left a baby on his doorstep.