One common theme is loyalty. The twin brother is always loyal to Harry, standing by him no matter what. For example, in many of these fanfics, when Harry is wrongly accused, the twin brother is the first to defend him.
I've also heard of 'Twin Guardianship'. In this fanfic, the twin brother is more attuned to the secrets of Hogwarts. He discovers hidden passages and rooms that can be used as safe havens for Harry. He also forms alliances with some of the more mysterious creatures in the school grounds to keep an eye on Harry from all angles.
He could be very brave. Just like Harry, but perhaps in a more understated way. He might not be the 'chosen one' but still jumps into danger to protect his brother.
One such fanfic could be 'The Twin's Bond'. In this story, Harry's twin brother is always by his side, protecting him from the various threats at Hogwarts. He uses his unique magical abilities, which he has developed through secret training, to keep Harry safe.
Well, a cool plotline could be that the twin brother has a relationship with a character that Harry doesn't really interact with much in the original series. Say, he becomes friends with a Slytherin who has a different view on the wizarding world. This friendship could bridge the gap between the houses in a way that Harry's relationships in the original story don't. It could also lead to the twin brother having a different perspective on the ongoing conflict between good and evil in the wizarding world.
Obviously, Harry and his twin brother are the central characters. But other popular characters can include Hermione and Ron. They might interact with the twin brother in different ways compared to how they interact with Harry. For example, Hermione might help the twin with his studies more because he has a different learning style. Dumbledore is also often a key figure. He could have different plans for the twin brother, like entrusting him with a special mission that is different from Harry's.
In some versions, Neville could also be one of Harry's protective mates. Neville, who grows in courage throughout the series, would be willing to stand up against any threat to Harry. And Luna, with her unique perspective and magical abilities, might also be part of Harry's protective group.
One common theme is loyalty. The older brother is always loyal to Harry and will do anything to protect him. Another theme is family love. Despite the difficult situations they are in, the bond between the brothers is strong.
One common theme is the exploration of family bonds. Since they are twins, the fanfictions often delve into how their relationship is different from normal siblings. Another theme could be competition. They might compete with each other in Pokemon battles or in achieving certain goals in the Pokemon world.