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.
Well, it could be that he's bored with his own dark plans. Fanfiction offers a whole new world of possibilities that he may not have considered. He could be intrigued by the different plotlines, characterizations, and relationships in the fan - made stories. Maybe he sees it as a way to study the human psyche, as fanfiction often reflects the desires and ideas of the fans. Or it could be that he's secretly envious of the freedom and creativity that the fans have in creating these stories, something he doesn't have in his own life of dark magic and power - seeking.
One reason is their similar origins as orphans. This common starting point sets up a parallel. Also, their connection to Hogwarts as a place of power and learning is significant. Another aspect is the power they both possess in magic. Tom Riddle was extremely powerful, and Harry also has great power within him. Their relationship as the hero and the villain can be seen as a fanfiction - like exploration of two extreme paths that could be taken from a similar starting point.
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.
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.
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.