In such a fanfiction, Harry might gain access to ancient magic knowledge. The founders, being from a different era, could teach him things not available in his own time. He may also experience a very different Hogwarts, perhaps one more in line with the founders' original vision.
If Harry was adopted by the founders in fanfiction, it would completely change the story's dynamic. He'd likely be exposed to a purer form of magic. Maybe he'd be taught in a Hogwarts that was still in its infancy, and be part of building the school's traditions. His relationships with other characters would be different too. Instead of having Ron and Hermione as his closest friends from the start, he could befriend students from different eras who were also learning under the founders.
Well, it would be a very interesting story. Harry would be exposed to a much more primitive form of magic. The founders could give him access to magic that has been lost over time. He might grow up with a stronger connection to the roots of Hogwarts. Also, there could be conflicts among the founders on how to raise Harry. Godric might want him to be a fearless warrior, while Salazar could have other ideas about his future. This would create a lot of drama and tension in the story.
In the context of the Harry Potter universe, the founders are Godric Gryffindor, Salazar Slytherin, Rowena Ravenclaw and Helga Hufflepuff. In this fanfiction, it's likely these are the founders who are training Harry.
His personality might become more traditional in some ways. Since the founders are from an earlier time, their values could rub off on him. He might be more reserved like some of the older wizards.
His personality would likely be a blend of the values of the founders. He'd be extremely courageous like Gryffindor, having that boldness instilled in him from a young age. At the same time, he might also possess Slytherin's cunning, being able to think on his feet in difficult situations. Ravenclaw's influence would make him more intellectually curious, always seeking knowledge. And Hufflepuff's teachings would ensure he was kind - hearted and loyal. Overall, he'd be a more well - rounded wizard with a complex personality.
His personality would likely become more self - assured. Growing up with the founders, he'd be constantly exposed to great magic and wisdom, which would boost his confidence. He might also be more independent as he'd be trained in a more solitary way by the founders.
It could be Harry Potter himself. Since he has so many special qualities and a deep connection to Hogwarts, he might be revealed as an heir. Maybe he has some latent powers related to one of the founders that haven't been discovered yet.
In a large number of fanfictions, Harry is indeed made to be descended from the founders. This concept allows for a great deal of creativity. It could mean that he has an innate understanding of the magic that the founders were known for. Maybe he has a natural affinity for the secrets of Hogwarts if he's related to Helga Hufflepuff, or perhaps he has a more political influence within the wizarding world if his ancestry is linked to Rowena Ravenclaw. Fanfiction writers use this idea to expand on the existing Harry Potter universe in unique and exciting ways.
Without more context, it's impossible to say who exactly these founders are. They could be founders of a small online Harry Potter fan community, or perhaps founders of a local Harry Potter reading group that also dabbles in fanfiction.