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.
A possible plotline is that the twin was separated from Harry at birth for some mysterious reason. Maybe a dark wizard wanted to use the twin's power for his own evil purposes. Years later, when they meet at Hogwarts, they don't recognize each other at first. But as they start to get to know each other, they sense a strange connection. This discovery could then lead to a journey of uncovering their past and their true family history. Along the way, they would face many challenges together, both from within the school and from the outside forces that are still interested in the twin's power.
One interesting plotline could be the twins getting involved in a time - traveling adventure within the wizarding world. They might use their signature prank - skills to outwit dark wizards in different eras.
Another plot could be centered around rivalry. The twin might be jealous of Hermione's popularity at Hogwarts. So, they start competing in various aspects, such as in Quidditch (even if Hermione isn't really into it, the twin could be). This rivalry could cause some tension between them, but eventually, they would realize that they are stronger together and reconcile.
Another plotline could involve the relationship between the twin and Harry. At first, there might be jealousy or misunderstanding due to the neglect the twin has faced. But as the story progresses, they could come to understand each other and work together to face the threats in the wizarding world. The twin could bring a new perspective to Harry's battles, and together they could be an even more powerful force against the dark side.
One interesting plotline could be the twin sister having a unique magical ability that Harry doesn't. For example, she might be able to communicate with magical creatures in a way no one else can. This could lead to her getting involved in adventures that are separate from Harry's at Hogwarts, but still end up being connected in some way, like when she discovers a secret about a creature that is related to a dark wizard who is also after Harry.
One interesting 'Harry has a twin' fanfiction could be where the twin has a different magical ability that complements Harry's. For example, while Harry is good at Defense Against the Dark Arts, the twin might be excellent at Potions and they work together to solve various mysteries at Hogwarts. Another could be a story where the twin was separated at birth and raised in a different magical culture, like the Beauxbatons Academy, and then they reunite at Hogwarts and have to adjust to being siblings.
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.
Well, perhaps a good plotline would be Percy's twin sister getting kidnapped by a powerful enemy. Percy then has to embark on a dangerous quest to rescue her. Along the way, he discovers more about his sister's hidden strengths and her importance in a prophecy. Or, they could both be sent on separate quests by the gods, but find out that their quests are actually intertwined and they need to work together to succeed in the end.
One interesting plotline could be the brothers having a secret mission within Hogwarts that the original books didn't cover. For example, they might be on a quest to find a hidden magical artifact that has been lost for centuries. Another could be their relationship dynamic affecting the course of major events in the wizarding world, like how they interact with Harry and his friends during the Triwizard Tournament.
One interesting plotline could be the twin sister using her unique bond with Harry to help him in his battles against Voldemort in ways that others can't. For example, she might have a special magical ability that is only enhanced by their twin connection.