One example could be that Snape secretly helps Harry with his Potions work. He might leave some useful hints or books where Harry can find them. Maybe he gives Harry a potion ingredient that is hard to get when he sees Harry struggling to complete a difficult potion recipe.
In the fanfic, Snape could be kind to Harry by protecting him from other Slytherins who might bully him. He could use his authority as a teacher and his position in Slytherin house to make sure that no one harasses Harry in the corridors or in the common room areas.
One possible reason could be his lingering resentment towards James Potter, Harry's father. Snape and James had a long - standing feud during their school days. Since Harry looks a lot like James, Snape might be transferring his old grudges onto Harry.
In some fanfictions, Snape's impulses towards Harry can be complex. One common portrayal is that his lingering love for Lily extends to a sense of protectiveness over Harry. He might have an impulse to keep Harry safe from the real threats in the wizarding world, even if he doesn't show it openly. This is often a way for fanfiction authors to explore the deeper, unspoken emotions Snape could have had for Harry based on his relationship with Lily.
One possible reason could be that in the fanfic, Snape realizes Harry has more of Lily in him than he initially thought. Harry might show kindness or a particular trait that reminds Snape of Lily, softening his feelings.
One common reason is Snape's lingering hatred for James Potter. Since Harry looks so much like his father, Snape might take out his old grudges on Harry. He sees James in Harry and can't help but be reminded of the past bullying and his unrequited love for Lily. So, he acts hurtfully towards Harry as a way to get back at James, even if it's not really fair to Harry.
At first, Harry might be very suspicious of Snape's kindness. After all, in the original story, they had a rather tense relationship. But as Snape continues to be kind, Harry starts to see him in a new light. He begins to trust Snape more and more.
One great example could be 'A Different Sort of Guidance'. In this fanfic, Snape takes Harry under his wing in a more private and reluctant way. He starts to teach Harry about advanced potions and also imparts some of his knowledge about the Dark Arts, not to encourage Harry to use them, but to understand the enemy better. Another is 'Snape's Unlikely Apprentice', where Snape is forced to mentor Harry due to a magical decree, and their relationship develops from one of mutual dislike to grudging respect.
In certain fanfic scenarios, Snape may feminize Harry by influencing his appearance. Maybe he gives advice on clothing or grooming in a way that makes Harry seem more feminine. For instance, suggesting a more delicate style of robes or a different hairstyle that is associated with femininity in the wizarding world.
One possible reason could be that in the fanfiction, the author might explore Snape's complex past with Harry's mother, Lily. Snape's love for Lily could translate into a more nuanced view of Harry. He may see parts of Lily in Harry and that softens his hatred.
In some fanfics, Snape might punish Harry because of his perceived insolence in class. Harry has a rebellious streak, and Snape, being strict, wouldn't tolerate any behavior that he deems disrespectful to his authority as a teacher.
At first, Harry is likely to be angry. He might feel that Snape is being unfair and targeting him. Harry has a strong sense of justice, and when he believes he's being wrongly punished, he'll be resentful.