Well, perhaps in the fanfiction, Snape discovers Harry has a special magical ability that is both a danger and a great potential. As a 'daddy' figure, he has to guide Harry in controlling it without alerting the wrong people. He might take Harry on secret excursions to practice this ability in safe places.
One possible plot could be Tucker and Ben getting into a friendly competition over a girl they both like in the fanfiction world. They might start off trying to outdo each other in impressing her, but then realize they value their friendship more.
One interesting plot could be where Edward has to adjust to sudden fatherhood while still dealing with his alchemical pursuits. Maybe he discovers a new form of alchemy related to protecting his child.
One common theme is protection. Snape often takes on the role of protecting Harry from the various threats in the wizarding world. Another theme is the discovery of family. Since Harry lacks a proper family in the original story, in these fanfictions, Snape can become a surrogate father figure, and there are themes of love and care that come with that new family dynamic.
Well, one possible plot could be about the challenges of raising a child in the world of Twilight. Maybe the baby daddy is a vampire and they have to deal with the baby having some special abilities or needs because of its vampire heritage.
One interesting story could be where baby Harry is found by Snape instead of Hagrid. Snape, initially reluctant, starts to develop a soft spot for the baby as he realizes Harry is just an innocent child. Another might be a story where baby Harry shows some early magical abilities that Snape is the first to notice, leading to a strange bond between them. And there could also be a fanfiction where in an alternate universe, Snape takes on the role of Harry's protector from a very young age, teaching him magic in secret.
Well, a common plotline is that Snape is initially reluctant to be around baby Harry due to his hatred for James. But as he spends time with the baby, he starts to see Lily in Harry. He might start to protect Harry not just for Lily's sake, but also because he begins to care for the child himself. Some fanfictions also explore how Snape's interactions with baby Harry might change the future events in the wizarding world, like how it could affect Harry's relationship with Snape when he grows up.
One interesting plot could be that Snape, in raising Harry, discovers a new side of the boy. He realizes that Harry has a natural talent for potions that was overlooked. Snape starts to teach Harry advanced potions techniques, and they form a sort of begrudging respect for each other. Harry begins to understand Snape's past and why he was so bitter, which changes their relationship for the better.
Perhaps in this fanfiction, Harry discovers some secrets about his parents from Snape that Dumbledore had been keeping from him. This could lead to a whole new understanding of the wizarding world's politics and relationships. Snape could be forced to protect Harry not just because of his loyalty to Dumbledore, but also because of his newfound connection with Harry.
Well, in some fanfictions, Snape trains Harry to master the art of non - verbal spells more effectively. This gives Harry an edge in duels. Also, there could be a plot where Snape trains Harry in the history of dark magic not to use it, but to better defend against those who do. It's a way of making Harry more well - rounded in his magical knowledge.
One interesting plot could be Snape taking in Harry after the death of Sirius. Snape, despite his initial reluctance, realizes he has a responsibility. He starts to train Harry in advanced potions and dark arts defenses in secret. This could lead to a unique bond between them as they gradually understand each other better.