Yes, there are some. Some explore the idea by creating a unique alternate universe where Hermione and Snape form an unlikely bond. They might rewrite the Hogwarts timeline and events to make their relationship seem more plausible.
There probably is. The world of fanfiction is vast and diverse. Writers like to play around with different character relationships. For 'Hermione is Snape's mate' fanfiction, it could be interesting to see how they handle the age difference, their different personalities, and the fact that they are from different Hogwarts houses. It might not be a common pairing in the official Harry Potter lore, but in fanfiction, anything is possible.
In some fanfictions, Snape is made out to be Hermione's father. Fanfiction writers often like to play with established relationships and create alternate backstories. This idea might be appealing as it adds a new layer of complexity to both characters' stories. It can lead to different interpretations of Snape's actions towards Hermione in the original series, like perhaps his strictness was a way of protecting his secret daughter in a way.
There could also be a fanfiction where Snape and Hermione are both involved in a mystery within Hogwarts. They are forced to work together to solve it. Along the way, they learn more about each other's strengths and weaknesses. Snape might be impressed by Hermione's deductive skills, and Hermione might gain a new perspective on Snape as they collaborate.
In the fanfiction, the relationship may start off with Snape being rather cold and distant towards Hermione as his familiar. However, as Hermione proves herself time and again, perhaps by using her unique skills to solve problems that Snape couldn't on his own, he starts to warm up to her. Their relationship then develops into a more complex one, where they have a mutual respect and a sort of unspoken understanding. This could involve Snape sharing some of his own magical knowledge with Hermione in a way that he would never do with other students, and Hermione in turn, helping Snape with his personal and professional matters, such as dealing with the other Hogwarts faculty or protecting the school from hidden threats.
I'm not entirely sure if there are a great number of fanfictions specifically about 'Snape fists Hermione'. But if you think about it, it could potentially be a part of a story where Snape has some sort of physical reaction or moment related to Hermione. Maybe it's in a situation where he's trying to protect her in a very physical way, and the idea of his fists comes into play. But again, finding such a specific story would require a lot of searching through different fanfiction repositories.
She might use her extensive knowledge of magic. For example, she could brew a complex potion that cures a deadly curse Snape has been afflicted with. Hermione is known for her academic excellence in potions, so it's very likely she'd use this skill to save him.
One great Snape and Hermione fanfiction is 'The Unbreakable Bond'. In this story, Hermione discovers a hidden side of Snape during her research in the Hogwarts library. Their relationship starts as a mentorship but gradually evolves into a deep friendship that defies the expectations of the wizarding world. It beautifully portrays their individual characters and how they can complement each other.
Maybe Snape is involved in some sort of mystery or danger within Hogwarts that has to do with magic spells. Hermione, with her vast knowledge of spells and her in - depth study of the Hogwarts library, could be a great help to him in deciphering old spells or magical texts related to the situation.