They would have a complex relationship. Snape would be a tough mentor, and Harry would likely resent his strictness at times. But Snape's knowledge and skills would also be something Harry would admire. There would be moments of tension, but also moments of connection, like when they work together on a difficult spell or potion. Over time, they could form a bond based on mutual growth and understanding.
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.
The development could also be due to the way the author writes Snape's backstory in the fanfic. If the author delves deeper into Snape's past, his difficult childhood, and his love for Harry's mother, Harry might start to understand Snape better. This understanding leads to admiration as Harry realizes that Snape is not just the strict and seemingly cruel professor he thought he was.
Initially, the relationship is one of captor and captive. Snape is in control and Harry is the unwilling victim. But as the story unfolds, Harry might begin to question Snape's motives. Snape, in turn, might start to open up a bit about his reasons for taking Harry. This could lead to a slow transformation of their relationship. They might find common ground in their shared experiences, such as both having lost people they loved to Voldemort. This newfound connection could start to heal the rift between them.
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.
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.
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.
As the story progresses, they might start to work together more closely. Snape could be teaching Harry some advanced magic that no one else knows, and through this process, they build a bond. Harry begins to understand Snape's past better and realizes that they have more in common than he thought, like their love for Lily Potter in different ways.
The relationship would start off rocky. Snape would be resistant to Harry's kindness as he has always seen Harry as James Potter's son. But Harry's persistent efforts to understand and help Snape would gradually break down Snape's walls.
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.