Communication is key. Maybe they start talking about their families. Harry shares his memories of his parents, and Snape shares his own difficult past. Through these conversations, they begin to understand each other on a deeper level and their relationship gradually shifts from hostility or indifference to something more like comradeship or even friendship.
It could also develop through shared experiences. For instance, if they are trapped in a dangerous place with various magical traps. They have to help each other out, like when Harry is about to be hit by a spell from a trap and Snape jumps in to protect him. This act of self - lessness can start to change their relationship for the better.
In some fanfics, at first it gets worse. Harry might start to fear or hate Snape even more after being hurt. But as the story progresses, there could be a turning point. Maybe Harry discovers Snape's real motives behind the hurt, like if Snape was trying to protect him from a greater danger in a very roundabout way. This could lead to a begrudging respect or even an odd sort of friendship in the end.
The relationship would be a rocky one. Snape has his past grudges against Harry's father. However, living together, they would be forced to interact daily. Harry might start to understand Snape's difficult past and Snape could see Harry's potential. There could be moments of anger, but also moments of mutual understanding, like when Harry helps Snape with some magical experiment.
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.
At first, it's often rocky. Harry is used to seeing Snape as an enemy, so he's very distrustful. Snape, on the other hand, has his own grudges against Harry's father. But as the mentoring progresses, Harry starts to see Snape's knowledge and skills. For example, Snape might teach Harry a difficult potions technique, and Harry realizes Snape is a great teacher. Snape, in turn, may start to see Harry as more than just James Potter's son, and their relationship slowly improves.
One plot idea could be that while trapped, they are forced to confront their past misunderstandings. Snape might reveal some of his long - held secrets about protecting Harry all along. For example, he could disclose the real reasons behind his actions that Harry had misinterpreted for so long.
In fanfiction, their relationship can develop in many ways. Sometimes it starts with Harry being suspicious of Snape as in the original books, but then Snape shows his selfless side. For example, he might save Harry from a dark spell and that starts to change Harry's view.
At first, it would be really rocky. Harry would be suspicious of Snape and Snape would be his usual grumpy self. But over time, as they get to know each other better, they might start to respect each other. Harry could learn about Snape's past and his complex relationship with his mother, which might soften his view of Snape.
Well, initially, Harry might be resistant to the idea of being adopted by Snape. He may think it's some sort of trick. But Snape, with his own sense of duty and newfound affection for Harry, tries to break through that resistance. As they spend more time together, Snape might share his own experiences at Hogwarts when he was a student, which helps Harry relate to him. And Harry, in return, might show Snape the good qualities he has inherited from his mother. This exchange of vulnerabilities and shared experiences gradually deepens their relationship into something more like a real father - son relationship.
At first, it's likely to be very tense. Snape has always had a grudge against Harry because of his father. But as they live together, they start to see each other's true selves. Harry might see Snape's vulnerability and intelligence, while Snape might see Harry's courage and determination that are different from James's arrogance.
Often, it starts with intense dislike. Snape is constantly critical of Harry in class, deducting points for the slightest mistakes. Harry, in turn, sees Snape as a bully. As the story progresses, there might be small moments of grudging respect, like when Harry realizes Snape's intelligence in potions, but the overall hatred remains for a long time.