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.
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.
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.
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.
Hermione got a Time - Turner in the Harry Potter series. It was a very special device that allowed her to go back in time. This was crucial for her to attend more classes than were physically possible at once. For example, she was able to take both Muggle Studies and Ancient Runes at the same time slot. It also played a significant role in some of the adventures she had with Harry and Ron, like saving Sirius Black and Buckbeak. The Time - Turner was a magical yet dangerous object, as misusing time - traveling magic could have disastrous consequences, but Hermione managed it quite well most of the time.
Snape would have more opportunities to right his wrongs. For example, he could go back and be more honest with Lily about his feelings. His character could become less bitter as he gets a chance to change things that made him so resentful in the first place.
In fanfiction, Hermione's Time Turner often leads to really interesting plot twists. It allows her to be in two places at once, which creates a whole new set of adventures. For example, she might use it to study more subjects than she could normally, but then get caught in a time - loop where she has to solve a mystery that's causing the loop.
One popular author is 'TimeTravellingWizard'. Their stories often have really detailed descriptions of how the Time - Turner works and the implications of time travel. They also write great character interactions, especially for Hermione.
One great fanfiction could be where Hermione travels back in time and tries to understand Severus better. She might see his early years at Hogwarts and how he was bullied. This could lead to her having a newfound respect for him and trying to change his fate in some way.
In some fanfics about Hermione and the Time Turner, it's often used as a plot device to fix mistakes. Maybe she goes back in time to prevent certain events from happening that had negative consequences in the original timeline. This can create a lot of interesting alternate storylines. For instance, she could stop the basilisk from being set loose too early, or she could change how she first met Harry and Ron, leading to different relationships and character developments.