Well, it could be that Snape fantasizes about Hermione's kindness and how it could impact the wizarding community. In his mind, he pictures her using her compassion to heal the divides between different wizarding groups. He might also fantasize about Hermione's thirst for knowledge rubbing off on other students, creating a more studious environment at Hogwarts. And he could be thinking about how she might one day use her knowledge to protect the wizarding world, like he has tried to do in his own way.
Maybe Hermione is injured while exploring some dangerous magical ruins. Snape is the only one around with the knowledge and power to heal her. As he heals her, they start to have deep conversations about magic, life, and their respective pasts, which in turn builds a connection between them.
There are likely some out there. Fanfiction is a vast genre, and while the idea of Snape fantasizing about Hermione might seem a bit odd at first, it could be re - imagined in a way that is family - friendly. Maybe it's a story where Snape has a dream about Hermione achieving great things in the wizarding world and he is sort of proud in a way, more like a teacher - student relationship in his thoughts.
One possible plotline could be that Hermione is forced to work under Snape in a special project. She initially resists his strict methods but gradually comes to understand his perspective and submits to his more experienced guidance in potions or some other area of magic. For example, Snape might be in charge of a top - secret research project and Hermione, with her brilliant mind, is chosen to assist. Through their interactions, she realizes that his seemingly harsh demands are actually aimed at achieving the best results.
One possible plotline could be that Hermione discovers a way to time - travel and goes back to Snape's childhood. She decides to raise him in a more positive environment to change his future. Maybe she teaches him about love and friendship from a young age, which alters his personality and his relationship with others at Hogwarts later on.
It could start with Snape having to supervise Hermione during detention. Instead of the usual harsh treatment, he notices her reading an advanced Potions book. He starts a conversation about it and realizes how deep her understanding is. This makes him see her in a new light. From there, he begins to offer her extra - curricular study opportunities, and slowly a friendship forms as they exchange ideas and learn from each other.
One reason could be the complex relationship between them. Snape's mixed feelings of resentment and a strange sense of protectiveness towards Harry in the original series can be explored more deeply in fanfiction through fantasies. Another reason might be the popularity of both characters. Fans want to see different interactions between them that were not fully shown in the books.
A really interesting plotline is when Snape and Hermione are brought together by a time - travel incident. In this scenario, they have to work together to fix the disruption in time, and in the process, they gain a new respect for each other. Also, there are plotlines where Hermione discovers Snape's hidden talents outside of teaching, like his skills in ancient magic or his connection to some long - lost magical artifacts, which leads to an interesting adventure between them.
Perhaps in a fanfiction, Snape's fists are a part of a memory. For example, Hermione discovers a memory of Snape's past where his fists were involved in a fight related to something that would later impact his relationship with her. It could be a way to explore his character's backstory and how it ties to Hermione.
Perhaps in a plot where there's a time - travel twist. Hermione is sent back in time and some ancient magic forces her to touch Snape as a way to set off a chain of events that will change the future of Hogwarts. It could also be that a magical artifact has some sort of hold over Hermione and compels her to touch Snape, and through this, she discovers some long - hidden secrets about Hogwarts or Snape himself.
One possible plotline could be that Hermione discovers a hidden side of Snape during her research in the library. This could lead to a series of conversations where Snape starts to see Hermione in a different light, not just as another student. Another could be that in a dangerous situation, Hermione and Snape are forced to work together, and through this experience, they develop a newfound respect for each other.