Maybe Harry's sister was hidden away for her own protection, and when she finally comes into the wizarding world, she has a different view of magic compared to Harry. She could be more interested in the academic side of magic, and through her research, she uncovers a plot by a group of dark wizards that Harry and his friends then have to stop. This could also lead to her having a different group of friends, which could introduce Harry to new perspectives and alliances.
In some fanfictions, Harry's sister might be sorted into a different house than him, like Slytherin. This would create a lot of internal conflict within the family as well as at Hogwarts. It could lead to a situation where Harry has to defend his sister against the prejudices of his friends. Or perhaps she has a prophecy related to her that ties into Harry's own destiny, and they have to figure out how to fulfill both prophecies without sacrificing one another.
One interesting plotline could be the main character using their wishes to change some of the major events in the Harry Potter universe. For example, they might wish to prevent certain characters from dying. Another could be using a wish to gain a special power that helps them in their adventures at Hogwarts, like being able to communicate with magical creatures more easily.
A more complex plotline could involve the sister being targeted by Voldemort because he sees her as a threat to his plans. She might have a prophecy associated with her that predicts she will be the one to finally defeat him. This would put her in a lot of danger and force Harry to be even more protective of her while also relying on her unique skills to fight against the Dark Lord.
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 birthday wish could be to receive a magical creature like a Hippogriff. In Harry Potter fanfiction, characters often have a deep longing for unique and dangerous magical creatures. Another wish might be to get a time - turner so they can relive certain moments or study more magic. And a third could be to be accepted into a secret and powerful magical society within Hogwarts, like the fabled Order of the Phoenix.
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.
One interesting plotline could be the twin sister having a special 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 help Harry in his fight against Voldemort in a different way than in the original books.
One interesting plotline could be the twin sister having hidden magical powers that are different from Harry's. For example, she might have an affinity for ancient spells that have been long forgotten in the wizarding world. Another could be that she was separated from Harry at birth due to a prophecy that the dark forces were after her specifically, and she grows up in a different magical community, unaware of her true identity until later in the story.
Maybe the forgotten sister discovers she has a connection to an ancient and powerful magic that was thought to be lost. As she uncovers this connection, she has to deal with the jealousy and suspicion of some in the wizarding world who fear her newfound power. She then has to prove that she will use it for good, like Harry does with his own powers.
In some fanfics, the sister could be a key to unlocking an ancient magic that has been forgotten. Her presence in Hogwarts might stir up old secrets and prophecies. The story could revolve around how she and Harry work together to figure out this new magic and use it to defeat the dark forces.
It could be a dark wizard who wants to use Harry's sister for some dark magic purpose. Maybe he believes that her blood or her unique magical essence can be used to open a portal to a world of dark magic or to resurrect an even more powerful dark force. This antagonist would stop at nothing to get his hands on her.