Well, in some fanfics, their relationship can be portrayed as a mentor - mentee relationship in reverse. Instead of Dumbledore mentoring Harry, Harry could try to mentor the young Tom Riddle. Harry would use his own experiences of overcoming darkness to guide Riddle away from the path of evil.
Well, in some fanfics, Tom Riddle is portrayed as having a bit more humanity. Maybe he has a love interest that makes him question his dark ways. This is different from the books where he seems fully committed to the dark side from a young age.
Well, in some fanfics, the relationship is depicted as a strange sort of friendship. They find common ground in their love for magic knowledge. However, there are also fanfics where Tom Riddle is obsessed with Harry Potter from the start, not just as an enemy but in a more psychological way. He sees Harry as a symbol of everything he could have been if he had made different choices.
Well, in some fanfictions, Tom Riddle could be developed as having a bit of a conscience from the start. Maybe the diary contains some part of his soul that wasn't fully corrupted yet. So instead of being purely evil, he has moments of hesitation or confusion about his actions.
One way to develop their relationship is through a magical accident. Suppose a spell backfires and links their minds in some way. Now they can experience each other's memories and emotions. Harry experiences Tom's difficult childhood, which makes him more sympathetic. Tom, on the other hand, gets a glimpse of Harry's future and the destruction he causes as Voldemort. This shared experience could be the starting point for a complex relationship where they both try to change the future and the past. They might argue, they might cooperate, but through it all, they are constantly learning about each other and themselves.
As the story progresses, their relationship could become more complex. Harry might become a father figure to Tom, teaching him right from wrong. Tom, on the other hand, could start to see Harry as someone he can rely on, but also struggle with his own inner demons that might pull him away from Harry's influence.
One plot idea could be a time - travel fanfic where Harry Potter goes back in time and tries to prevent Tom Riddle from becoming Voldemort. He could attempt to befriend the young Riddle and guide him towards a different path, perhaps by showing him the value of love and friendship early on.
The relationship could be shown as a mentor - mentee type in some fanfictions. Maybe the Dark Lord, in an alternate reality, decides to teach Harry some of his dark magic knowledge not to corrupt him, but to make him stronger to face other threats in the wizarding world. This would completely change the dynamic between them. They could also be shown as reluctant allies, forced to work together to stop a greater evil that is emerging in the wizarding world. This would involve a lot of tension and distrust between them at first, but gradually they could start to understand each other more.
One unique way is through a shared secret. For example, Fem Harry discovers a hidden part of Hogwarts that is related to a powerful and ancient magic. Tom Riddle also stumbles upon this secret. Instead of fighting over it, they decide to explore it together. During this process, they rely on each other's skills and knowledge. This shared adventure builds a deep bond between them, and they start to see each other in a new light, far from their initial impressions.
At first, it might be rocky. Tom would be suspicious of Harry's intentions. But as Harry shows him genuine care, Tom would start to open up. Eventually, they could become like family, with Tom looking up to Harry as a role model.
They could be portrayed as having a bit of good in them. For example, they might be under some sort of dark spell that forces them to act as they do, and if that spell is broken, they could be more like guardians of the wizarding world in a different way.