The fanfiction may show their relationship evolving into a mentorship of sorts. Snape, with his vast knowledge, could start guiding Harry in ways that were unthinkable in the original story due to their animosity. For example, Snape might help Harry with some advanced magic techniques or give him advice on dealing with the dark forces. This would completely change the dynamic between them from one of hatred to one of cooperation and growth.
It re - imagines their relationship as more of an understanding one. Instead of the constant hostility, they might start to have moments of mutual respect.