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 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.
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.
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.
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 great 'Harry Potter Tom Riddle Fanfiction' is 'The Heir of Slytherin's Redemption'. It shows a different side of Tom Riddle, exploring what could have happened if he had been given a chance at a different path. It has a really interesting plot that keeps you hooked from start to finish.
One popular idea in such fanfiction could be that Harry, through some magical time - turning or alternate reality scenario, discovers Tom Riddle before he fully becomes Voldemort. Harry might see the good in Tom that was lost over time and tries to prevent his fall to the dark side. Their soulmate connection could be a powerful force that draws them together, even as their destinies seem so opposed.
One great 'Harry Potter' Tom Riddle slash fanfiction is 'The Heir of Slytherin's Heart'. It delves deep into the complex relationship between Harry and Tom Riddle. The author does an amazing job of exploring their characters in a new light, with a plot that keeps you on the edge of your seat.
I'm not sure if it's popular. It's a rather niche and unusual concept, so it might not have a wide following. But in the world of fanfiction, there are always small groups of people interested in unique and out - of - the - ordinary ideas.
One popular type of fanfiction in this vein could be about Tom Riddle's interaction with magical creatures during his time at Hogwarts. Maybe he discovers a creature that has some connection to the dark arts and tries to use it for his own gain. For example, he might come across a basilisk in the Chamber of Secrets earlier than in the original story and attempt to control it to intimidate other students.