Well, one possibility is that it would create a huge conflict within the wizarding world. Harry is seen as a hero and Tom Riddle (Voldemort) is the ultimate villain. His daughter would be a very controversial figure. Harry might face a lot of opposition from his friends and the wizarding community at large.
In this kind of fanfiction, there could be a lot of magical elements involved in their relationship. For example, they might discover a new form of magic together that was previously unknown. Harry's Gryffindor values and her, perhaps, more complex heritage could combine in interesting ways. It could also lead to a re - evaluation of how the wizarding world views family and bloodlines, as Harry's decision to marry her would go against the traditional view of the pure - blood ideology that Voldemort adhered to.
Perhaps in this fanfiction, the daughter could be different from her father. She might have been raised away from Voldemort's influence. Harry could see the good in her and fall in love with her positive qualities. Their relationship could then be a way to bridge the gap between the two sides of the long - standing wizarding conflict.
The storyline could start with Harry encountering the daughter by chance. Maybe she's been in hiding all these years. He initially feels conflicted because of who her father was. But as he gets to know her, he realizes she's not like Voldemort at all.
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.
In a Tom Riddle x Reader fanfiction, they could meet in Hogwarts. Maybe the reader is a new student and catches Tom's attention with their unique magical abilities. This could lead to a series of interactions where Tom tries to figure out the reader's secrets.
Tom could manipulate Hermione. He is a very intelligent and cunning boy. He might see Hermione as a means to an end. Maybe he could use her knowledge of magic to further his own studies in the dark arts. He could pretend to befriend her while secretly plotting to use her magic for his own evil purposes. However, Hermione is also smart and would likely catch on eventually.
Family and heritage play a big role. She has to deal with the fact that her father is one of the most feared wizards in history. There's often a theme of secrecy as well. She might have to keep her true identity a secret from her friends. Also, power is a theme. As Tom Riddle was powerful, she may inherit some of that power and has to decide how to use it, for good or evil.
In fanfiction, Merope Gaunt and Tom Riddle Sr's story could be a tale of redemption. Maybe Merope realizes the wrong she has done in using a love potion on Tom and tries to make amends. She could attempt to win his love genuinely, without the use of magic. This would show her growth as a character and add a new layer to their relationship.
One plot idea could be Fem Harry growing up in the wizarding world with the secret of her parentage. She might start to notice strange similarities between herself and Tom Riddle's dark magic tendencies, but struggle against them. Another could be her discovery of her heritage leading to a conflict within the wizarding community, as some fear she will follow in her father's dark footsteps, while others believe she can break free from that legacy.
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 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.
An old Harry Potter fanfiction about Tom Riddle could be about his time as a young wizard trying to gain followers. He was a very intelligent and manipulative character. Fanfictions might explore how he used his charm and intelligence to persuade other students to his way of thinking. Maybe he starts a secret club where they study dark magic together, which is a precursor to his later Death Eaters.