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 such a fanfiction, one possibility is that Snape would initially struggle with his new role as an adoptive father. He has a complex personality, but over time he might start to show his protective side towards Harry and Hermione. He could teach them advanced magic, especially his own areas of expertise like Potions, in a more personalized way.
One interesting plotline could be Hermione's struggle to adjust to living with Snape. She's used to the warm and inclusive environment of Gryffindor, and Snape's dark and brooding personality makes it a big change for her. Another could be Snape seeing Hermione's potential not just as a student but as a daughter figure, and he starts to teach her advanced magic privately, which in turn helps Hermione to solve some of the school's mysteries.
Well, in this fanfiction, it might start with Snape finding Hermione as a baby in a dangerous place like the Forbidden Forest. He adopts her because he sees her potential even as a baby. As she grows, he teaches her magic in his own strict way, but also forms a deep bond with her. This could lead to some interesting interactions with other Hogwarts faculty who are surprised by Snape's new role as a father figure.
In this type of fanfiction, perhaps Snape initially stumbles upon Hermione being abused by some other students or even adults in the wizarding world. Feeling a sense of responsibility, he adopts her. Snape would introduce her to his world of potions and dark arts knowledge. Hermione's inquisitive nature would blend well with Snape's expertise. They might face challenges from the wizarding community who don't understand their relationship, but they stand strong together, with Hermione gradually learning to trust again and Snape becoming more open and caring.
At first, it would be really rocky. Harry has a history of distrusting Snape, and Hermione might be a bit cautious too. But as time passes, Snape's care for them in his own strict way would start to show. He'd probably be tough on them about their studies, but they'd see it's because he wants them to succeed.
Snape would become more nurturing. He's used to being cold and distant, but with a baby to care for, he'd have to soften. For example, he'd learn to comfort Hermione when she cries.
Snape's personality might soften. He's used to being cold and distant, but taking in Hermione could bring out his protective side more. He'd become more patient as he guides Hermione through her troubles.
It could be an orphaned wizard child from a family that was killed by Death Eaters. This would give Snape an added sense of responsibility as he might feel guilty for being associated with the Death Eaters in the past.
One possibility is that Snape would be extremely strict with them at first. Given his past relationship with Harry especially, he might struggle to show affection openly. But over time, he could come to understand the trio better. Harry would likely be the most resistant to Snape's parenting at the start, but as Snape showed his genuine care, Harry might warm up. Hermione would probably be eager to learn from Snape, seeing his vast knowledge. Ron, on the other hand, might find Snape's gloomy demeanor a bit off - putting, but with Hermione and Harry's influence, he'd also adapt.