At first, Severus might see Hermione as just another meddling student. But as they spend more time together through the time - traveling adventures, he begins to respect her. Hermione, on the other hand, starts to understand the complexity of Severus' character. She realizes that he is not just the brooding, mean professor she once thought. Their relationship could develop into a deep mutual respect and perhaps even a form of mentorship, with Severus guiding Hermione in some of the darker aspects of magic and Hermione helping Severus with his more emotional and social struggles.
Their relationship might start off very rocky. Severus would be distrustful of Hermione as she is a Gryffindor and he has his own prejudices. But as they are forced to rely on each other because of the Time - Turner situation, they start to see each other's strengths. For example, Hermione's intelligence and quick thinking, and Severus' knowledge of magic and his ability to be cunning in difficult situations.
Their relationship would likely start off with a lot of tension. Snape is used to being distrustful of Gryffindors, and Hermione is not one to take Snape's snide remarks lightly. However, as they are forced to interact more due to the Time - Turner situation, they might gradually develop a mutual respect. Hermione would come to understand Snape's complex past, and Snape would see Hermione's intelligence and determination.
At first, it might be a bit rocky. Hermione is very opinionated and Severus is, well, Severus. But as she grows, she could start to see past his prickly exterior. Maybe she discovers his hidden kindness through his actions towards her in the fanfiction.
In fanfiction, the Time - Turner can be a tool to bring Hermione and Snape closer. For example, if Hermione uses it to help Snape with a past event, he may start to trust her more. This newfound trust can change their relationship from one of animosity in the original story to a more collaborative and understanding one. They might share secrets and knowledge that they wouldn't have otherwise.
At first, their relationship would likely be very rocky. Severus would probably be cold and distant, still holding onto his Slytherin pride and past experiences with Gryffindors like Hermione. Hermione, on the other hand, would be confused and perhaps a bit angry about the arranged situation. But as time goes on, they might start to communicate more. Hermione's inquisitive nature could lead her to ask Severus about his past, and Severus might be reluctantly drawn into sharing some of his secrets. This sharing could be the start of a new understanding between them.
One idea could be that Hermione accidentally travels too far back in time with the Time - Turner and ends up in Severus' student days. She has to navigate Hogwarts without being detected while also trying to figure out how to get back. And Severus stumbles upon her and at first is suspicious but then realizes she's from the future and they start to work together to fix the time - line.
In the beginning, Severus would probably view Hermione as a nuisance. But Hermione, being Hermione, would not take being treated like a simple pet lying down. She would constantly challenge him in small ways, like refusing to follow his commands in a way that made him think. This would pique Severus's interest. As they spent more time together, he would come to respect her and see her as more than just a pet. Their relationship would develop into a complex one, with elements of friendship, respect, and a shared love for knowledge.
Their relationship could start with mutual respect for each other's intelligence. Hermione respects Severus's knowledge in potions and the Dark Arts, and Severus respects Hermione's quick learning and thirst for knowledge. This respect can gradually turn into a more affectionate father - daughter relationship as they spend more time together.
In these fanfictions, their relationship often starts with suspicion. Hermione is wary of Snape due to his reputation, and Snape initially sees Hermione as just another student. But as he starts to help her, like when he gives her advice on how to deal with a particularly tricky magical creature in Care of Magical Creatures class, she begins to see a different side of him. Their relationship then slowly develops into a mutual respect as they work together on various tasks around Hogwarts.
Their relationship might start off rocky because of their differences. But the phoenix could act as a sort of mediator. It could bring them together by leading them to a common goal, like protecting the phoenix's nest. As they work towards this goal, they might start to respect each other's skills and knowledge.
One great 'Time Turner Hermione' fanfiction is 'Hermione's Time - Turner Adventure'. It delves into Hermione using the Time Turner for more than just attending classes. The story is full of mystery and her character development is really interesting as she faces new challenges.