A fanfiction could revolve around a time - traveling plot. Harry goes back in time and sees Snape as a young student, and the cane that Snape later has as a teacher is actually a family heirloom. Harry then has to make sure that Snape doesn't lose the cane in a crucial moment in the past which could change the future of Hogwarts.
One interesting fanfiction could be where Snape uses his cane not as a tool of punishment but as a magical conduit in a situation where he and Harry have to work together against a new dark threat. In this story, the cane might hold secrets of an ancient magic that only Snape is aware of initially.
In some fanfictions, Snape's cane serves as a symbol of his authority. It can be used to intimidate Harry and the other students, like when he taps it on the floor to get everyone's attention. It represents his strict and often unapproachable nature.
One interesting Snape and Harry fanfiction could be one where Snape mentors Harry in a more private and less hostile way. They could bond over potions and Snape could finally see Harry as more than just James Potter's son.
One interesting Harry Snape fanfiction could be one where Snape adopts Harry after the death of his parents. In this story, Snape has to overcome his initial dislike for James Potter's son and gradually forms a unique bond with Harry. It shows a different side of Snape, his capacity for love and care that was hidden beneath his cold exterior in the original series.
One interesting Snape - Harry fanfiction could be where Snape finally reveals his true feelings about protecting Harry to him. Maybe in a moment of danger, Snape confesses that he was always secretly looking out for Harry because of his love for Lily.
Another type of fanfiction could be set in an alternate universe where Lucius has a different path. He could be a hero instead of a villain. In this story, he might use his knowledge of the Dark Arts not for evil but to fight against a greater, more menacing dark force. He could form alliances with characters he previously opposed, like the Weasley family, and together they battle this new threat.
One story could be about a headmistress who used a cane as a symbol of authority but never actually used it to punish. She just carried it around during school inspections, and the students were always on their best behavior out of respect for the cane's presence.
One interesting deaged Snape and Harry fanfiction could be about Snape being deaged to Harry's age and them having to work together on a special project at Hogwarts. They might start to see each other in a new light, away from their usual teacher - student dynamic.
One interesting story could be where Snape uses a collar on Harry as a form of magical protection. In this fanfiction, the collar might have special enchantments that keep Harry safe from dark magic. It could also be a symbol of Snape's hidden care for Harry, despite their often tense relationship in the original series.
One interesting aspect could be the exploration of Snape's complex character in a dominant role over Harry. It might show a different side of their relationship, perhaps with Snape guiding Harry in a more forceful way in magic studies. For example, he could push Harry to master difficult spells faster.
A really cool fanfiction could be set in an alternate universe where Harry, Snape, and Draco are all part of a secret society in Hogwarts. They have to keep the society's existence and purpose a secret while dealing with their own personal issues and rivalries within the group.