One common plot point is the exploration of their family history. How did they end up as brothers? Another is the change in Harry's upbringing, as Tom being his brother would likely have a big impact on his early life. Also, the relationship between them and how it affects the fight against Voldemort (Tom) in the wizarding world.
One common plot point is that they discover their relationship later in life. Maybe Harry has always felt a strange connection to Tom Riddle, and when they find out they're brothers, it throws both of them for a loop. Another could be that their shared heritage gives them some unique powers or abilities. For example, they might be able to combine their magic in a way that no one else can.
Well, often there's a plot point about how their family connection affects their relationships with other characters. For example, how their friends react to the news. Also, a common plot is that they inherit some sort of special family magic or legacy together. This could lead to adventures where they have to unlock the secrets of their family's past and use that knowledge to their advantage in the present.
Yes, there are such fanfictions out there. However, I can't really recommend specific ones as there are so many and their quality varies greatly. You can try searching on fanfiction - specific websites like Archive of Our Own or FanFiction.net using relevant keywords to find them.
One common plot point is that Harry often has to find a way to get past the Dementors in Azkaban. He might use the Patronus charm in a new and creative way. Another is that he usually has to overcome some sort of magical obstacle or security measure in the prison. And of course, there's always the emotional reunion between Harry and Sirius.
One interesting plot point would be the family secrets that come to light. If Harry is James' younger brother, there could be secrets about their family that were hidden from Harry before. For example, there might be a hidden magical inheritance or a prophecy that involves both of them. Another aspect could be the impact on Harry's friendships. His relationship with Ron and Hermione might change as he now has a different family identity. Also, the way the wizarding world views the Potter family as a whole could be altered. The Potter family might be seen as even more powerful or have different political implications. And finally, the emotional journey of Harry as he discovers more about his brother James and their family history could be a very engaging plot point.
In these fanfictions, the theme of acceptance is quite common. They have to accept each other as brothers despite their differences. Also, the exploration of the past is a big theme. Digging into their family's past to understand why things are the way they are in their present. And there's always the theme of adventure as they go on various magical adventures together as brothers.
Yes, in certain fanfictions Harry Potter is made out to be Tom Riddle's brother. This is often a way for fanfiction authors to add a new twist to the story. They might do this to explore how the two characters, with their very different natures (Harry being the hero and Tom being the villain), would interact if they had such a close family relationship. It also allows for new plotlines to be developed, like how their shared heritage could affect the wizarding world. But remember, it's all part of the fan - made world and not the official 'Harry Potter' story.
The impact on Harry's relationships is also a key plot point. His relationship with Dumbledore may change as the headmaster has to deal with Harry's new - found power through the peerage. His friendships, too, can be affected. Some friends might be jealous, while others might see it as an opportunity to further their own causes. And his relationship with the wizarding society at large can shift from being an outcast to a figure of power and influence.
Another theme is redemption. Some fanfictions try to show Tom Riddle's possible redemption through his relationship with fem Harry. They might explore how her presence and influence could change his path towards the dark side. It's an interesting concept as it gives a new perspective on the character of Tom Riddle.
One great plot point would be if the soulmate connection allows them to share each other's memories. Harry would see Tom's difficult childhood, which might make him more empathetic towards him. Tom, on the other hand, would see Harry's experiences of love and friendship. This could lead to a major change in Tom's character. Also, the plot could involve them trying to hide their relationship from Dumbledore, who might see it as a dangerous experiment that could disrupt the balance of the wizarding world.