Well, in the original series, Snape is often quite harsh towards Hermione and the other Gryffindors. But in a fanfiction where Hermione is a Snape fan, she would likely be more understanding and patient with him. Instead of being intimidated or annoyed by his behavior, she might try to find the good in him from the start.
Well, it often starts with a lot of misunderstandings. Snape has his own preconceived notions about Hermione as a Gryffindor student, and Hermione has her own view of Snape as a strict and often unfair teacher. However, as they live together, small moments start to change their relationship. For example, when Hermione is having trouble with a particularly difficult spell, Snape doesn't scold her but instead patiently guides her. This gradually builds trust between them, and they form a unique bond that is different from the typical student - teacher relationship or even a normal father - daughter relationship.
In the fanfiction, the relationship may start off with Snape being rather cold and distant towards Hermione as his familiar. However, as Hermione proves herself time and again, perhaps by using her unique skills to solve problems that Snape couldn't on his own, he starts to warm up to her. Their relationship then develops into a more complex one, where they have a mutual respect and a sort of unspoken understanding. This could involve Snape sharing some of his own magical knowledge with Hermione in a way that he would never do with other students, and Hermione in turn, helping Snape with his personal and professional matters, such as dealing with the other Hogwarts faculty or protecting the school from hidden threats.
At first, Hermione might be suspicious of Snape's new - found protectiveness. But as time goes on, she starts to see that he has good intentions. Snape, on the other hand, gradually warms up to Hermione more and more, sharing his knowledge and advice with her.
In the original series, Harry and Snape have a very tense and often hostile relationship. But in this fanfiction, their relationship is likely to be much more positive. Harry feeling safe with Snape means there is a sense of trust that was absent in the original.
The whole dynamic of the fight against Voldemort would shift. If Harry were Snape's son, Snape's loyalty and actions throughout the series would be re - evaluated. Harry might have access to different knowledge and skills that Snape could pass on. His connection to the Dark Arts might be more nuanced. Also, the way the other Hogwarts professors treat Harry would be different. They might be more cautious or more expectant of him, given his new family connection.
It completely changes the relationship dynamics. In the original story, Draco and Hermione are more like rivals. But in fanfiction where he cheats on her, it creates a whole new layer of animosity and heartbreak. Hermione, who is usually strong - willed, has to deal with the betrayal in a different way than she does with her academic or magical challenges in the original.
The concept often involves Snape having an upper hand in their relationship. He may be in charge of her training in some special form of magic. His dominance can also be emotional. He might be the one who decides when and how they interact. For instance, he could cut off communication if he feels Hermione is not following his instructions properly. This kind of control over their relationship and her growth as a witch is a common way the concept of Snape dominating Hermione is explored in fanfiction.
The relationship might start off on a rocky note. Snape, being strict, would be angry at Hermione's naughtiness. But as time goes on, he could start to respect her intelligence. For example, if she was naughty by trying to improve a potion in an unorthodox way, he might see her potential.
Hermione might become more guarded at first. She is used to being independent and suddenly being 'gifted' to Snape is a big change. But over time, she could learn to be more patient and understanding. Snape, on the other hand, might soften a bit. His usual cold exterior could crack as he gets to know Hermione better.
One possible fanfiction could be about Hermione discovering Snape's hidden past and his true motives. She might initially be skeptical but as she delves deeper, she realizes that Snape was more complex than she thought. For example, she could find out about his love for her mother's friend Lily and how that influenced his actions throughout the series.