In a fanfiction where Harry Potter never went to Hogwarts, he might be trained by a group of rogue wizards. These wizards could be against the traditional ways of Hogwarts. They could teach Harry some unique forms of magic that are not taught at Hogwarts. This would set him on a different path, perhaps making him an outcast among the traditional wizarding community, but also giving him a set of skills that are very different and powerful.
One possible plot could be that Harry Potter discovers a different magical school. Maybe he stumbles upon a hidden school in the Muggle world that has been secretly teaching magic. He could form new friendships and face different types of magical challenges there. It would be a completely new magical experience for him, away from the familiar Hogwarts environment.
One possibility is that Harry grows up in the Muggle world completely unaware of his wizarding heritage. He might lead a normal life, going to a regular school, making Muggle friends, and having no idea about the magical world that could have been his. Maybe he has a natural aptitude for something like martial arts or a particular academic subject that in the wizarding world would be replaced by magic.
Perhaps she discovers a different magical school or a secret magical community outside of the Hogwarts system. In this fanfiction, she could be mentored by an eccentric and powerful wizard who has his own way of teaching magic, far removed from the traditional Hogwarts curriculum.
The Dumbledore character could still be important. He might be secretly watching over Harry, guiding him from a distance. Another character could be a new wizard or witch that Harry meets in the Muggle world who has a special mission related to Harry. For example, a young witch who has been exiled from the wizarding world but has the knowledge to help Harry understand his powers. And of course, Voldemort would still be a main antagonist as his threat looms over the entire wizarding world whether Harry is at Hogwarts or not.
One possibility could be that Snape grows up in a different magical environment, perhaps in a small, hidden magical community that has its own unique way of teaching magic. He might develop his skills in potion - making and the Dark Arts in a more self - taught or community - guided way. Without the influence of Hogwarts, his relationships would be very different. He may not have the same intense rivalries or unrequited love for Lily Potter.
Hermione and Ron might not become friends in the same way. Since Harry was the catalyst for their friendship at Hogwarts, without him there, they might not cross paths as easily. Hermione could be more focused on her studies alone in a different school, and Ron might be stuck in his family's shadow without Harry to bring out his better qualities.
One possibility could be that Harry discovers he has some other magical destiny outside of Hogwarts. Maybe he is taken in by a different group of wizards who teach him their own brand of magic in a hidden location. They might believe Hogwarts is too mainstream or that Harry has a special power that needs to be nurtured away from the school.
The plot could develop with Harry being mentored by a solitary wizard or witch who doesn't believe in the Hogwarts system. They could teach him magic in a more unorthodox way. For example, instead of formal classes, he could learn magic through real - life experiences and solving problems in the wizarding community outside of Hogwarts. This would give him a different perspective on magic compared to the traditional Hogwarts - educated wizards.
Well, it could be about Harry facing an even greater threat than Voldemort. Maybe a new dark wizard emerges from the shadows and Harry has to use all his skills and the support of his friends to defend Hogwarts as its champion. He might have to go through a series of super - difficult challenges that test his magic, courage and loyalty to an extreme level.
One possible plot could be that Harry Potter, as the new owner of Hogwarts, decides to reform the school's curriculum. He might introduce new magic subjects that were previously overlooked, like ancient rune magic for practical applications.
Perhaps Harry is teaching Potions in the fanfiction. Since he had a bit of a rocky start with Potions in his student days, he could be a very understanding teacher. He might encourage students to experiment more, which is different from Snape's strict methods. He could also share stories about how important Potions were in his adventures, like when they made Polyjuice Potion. This would make the class more interesting and inspire students to take Potions more seriously.