One possible plot could be that Harry, using his knowledge of love and friendship, tries to teach Tom about the power of positive emotions. He might show Tom how his own journey was shaped by the love of his friends and family, in contrast to Tom's more solitary and power - hungry path. Maybe Harry takes Tom to Hogwarts in a time - travel like scenario and shows him the true meaning of the houses, not just the pursuit of power within Slytherin.
In this fanfiction, Harry might teach Tom about magic in a different way. Instead of just focusing on dark magic, Harry could show Tom the beauty and wonder of all types of magic. He could take Tom to see magical creatures and explain how they are an important part of the wizarding world. Harry could also try to make Tom understand that using magic for the greater good is far more rewarding than using it for personal gain.
A lot could occur. Harry might try to instill in Tom the importance of forgiveness. Given that Harry has forgiven many of his enemies, he could explain to Tom that holding grudges and seeking revenge only leads to more pain and destruction. For example, when he forgave Snape in the end.
Maybe Harry would teach Tom about the consequences of dark magic. Since Harry has faced Voldemort multiple times and seen the destruction caused by dark spells. He could use these real - life (well, in the wizarding world) examples to make Tom understand that there are other paths in magic that are more positive and life - affirming.
One possible plot twist could be that Tom Riddle discovers Harry has a hidden power that he didn't expect. Maybe Harry has the ability to resist Riddle's mind - control spells in a unique way. This could lead to a battle of wills between them where Harry tries to outwit Riddle while being held captive.
One possibility could be a story of internal conflict for Harry. He might struggle with the dark heritage from Tom Riddle while trying to uphold the values of the wizarding world he has grown to love. He could constantly battle his own darker instincts that come from being Voldemort's (Tom Riddle) son. For example, he might have an in - built talent for Parseltongue that he has to learn to control and use for good instead of evil.
Harry would be really interesting. He has to step into the role of a teacher, which is quite different from his usual role as a student or a hero. He has to figure out how to communicate with Tom, who is essentially the most evil wizard in history. Harry's own experiences with Voldemort give him a unique perspective, and seeing how he uses that to try and teach Tom would be fascinating.
One reason could be that he wants to find new ways to manipulate the story. Since fanfiction can be so diverse, he might be looking for ideas that he can use to his advantage. Another reason could be a strange form of entertainment. Even though he's a dark character, he could still find the creativity in fanfiction amusing or useful in some way. And maybe, just maybe, he has a hidden love for the world of Harry Potter that he doesn't show in the original story.
As the teaching progresses, they could develop a sort of mentor - mentee relationship. Harry would be constantly trying to steer Tom away from the Dark Arts, while Tom would be trying to learn as much as he can from Harry. However, there would always be an underlying tension because of Tom's future as Voldemort. Their relationship might be a complex dance of trust and suspicion.
One interesting plot twist could be that Hermione's teachings accidentally lead Tom Riddle to an even darker path. Maybe she teaches him advanced magic that he then uses in unexpected and malevolent ways. For example, he could use time - turning magic she showed him to manipulate historical events to his advantage.
One possibility is that Harry, having seen the dark path Tom Riddle took, decides to take him in early. He might teach Tom about love and friendship, things he lacked growing up. Harry could introduce Tom to the wizarding world in a more positive light, showing him the joys of Hogwarts and the value of good relationships, thus preventing him from turning into Voldemort.
One possible plot could be that Harry discovers some long - lost secrets about Tom Riddle's early days at school. Maybe he stumbles upon a hidden diary that reveals Riddle's true motives even before he became Voldemort. This could lead to Harry trying to prevent some of the dark magic that Riddle was starting to dabble in from ever happening.