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.
Good fanfiction in this area often has a strong plot. Maybe it's about Tom's discovery of his magical heritage, or how he starts to form his ideas about power. It should keep the reader engaged from start to finish, with twists and turns that make sense in the context of the Harry Potter universe.
One great aspect of Hermione and Young Tom Riddle fanfiction is the exploration of what could have been. Hermione's intelligence could potentially have an impact on Tom Riddle's early development. Maybe she could have seen the signs of his future dark path earlier and tried to steer him away.
Another plot is where Hermione is accidentally transported to Tom Riddle's time and has to navigate the Hogwarts of that era while dealing with the enigma that is young Tom. Their interactions can range from friendly debates about magic to more intense confrontations as Tom starts to show his darker tendencies.
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 popular young Tom Riddle fanfiction is 'The Heir of Slytherin's Ascent'. It delves into Tom's early days at Hogwarts, exploring his budding dark tendencies in a really engaging way.
You could also create a fanfiction where a new character, an orphan just like Tom, arrives at the orphanage. This new character could either be a positive influence on Tom, trying to show him kindness and friendship, or they could be in competition with him for the limited resources or attention in the orphanage. This would add a new dynamic to the story of Tom Riddle in the orphanage.
One challenge is staying true to the characters' personalities. Tom Riddle is already on a dark path as a young boy, so it's difficult to balance his malevolent tendencies with any potential for change or redemption in the fanfiction. For Harry, his natural instinct to oppose evil has to be reconciled with the idea of trying to help Tom.
One interesting aspect could be seeing how Tom Riddle's character develops differently. Maybe he gains new knowledge from the books that alters his path towards becoming Voldemort. For example, if he reads about friendship and loyalty in the books, it might make him question his own dark tendencies.
One common theme is redemption. Many fanfictions explore the idea of Harry trying to save young Tom Riddle from his dark future. Another theme is power. Since both Harry and Tom are powerful wizards, there are often power struggles or comparisons between them.