One possibility could be that she shows up at Camp Half - Blood unexpectedly. Maybe she was raised by a mortal family all this time, not knowing about her demigod heritage. When she arrives, she has powers similar to Percy's but also some unique ones, like the ability to communicate with sea creatures in a different way than Percy. This could lead to all sorts of adventures and conflicts within the camp as everyone tries to figure out who she really is and what her role will be.
You can start by giving her a distinct personality. If Percy is brave and impulsive, make her more cautious and calculating. For example, she could be the one who always thinks twice before jumping into a fight, analyzing the situation and coming up with a plan. This contrast in personalities can create interesting dynamics within the story.
One great 'Percy Jackson Twin Fanfiction' is 'The Twin Heroes of Olympus'. It follows the adventures of Percy's twin siblings in the world of Greek mythology. The story has exciting battles and interesting character development.
Another plot could involve the twin sister being cursed. This curse could be related to her connection with the sea as well. For example, every time she uses her powers related to the sea, she experiences a great deal of pain. Percy then has to find a way to break the curse. In the process, they discover an ancient prophecy that not only involves Percy but also depends on his sister's role in fulfilling it.
The character of Percy's twin sister can be developed by giving her unique personality traits. For example, if Percy is brave and impulsive, she could be more cautious and calculating. Her appearance could also be distinct, like having different colored eyes or hair. Additionally, her relationships with other characters in the Percy Jackson universe can help develop her. If she befriends Annabeth, for instance, it can show her intelligence and ability to form strong bonds.
Her character could develop in a way that is very much in contrast to Percy. While Percy is often impulsive, she could be more calculating. This difference causes some friction at first, but as they face challenges together, they learn from each other. For example, she might teach Percy to think before he acts in some situations, and Percy could show her how to be more spontaneous and trust her instincts. Over time, she becomes more well - rounded, balancing her cautious nature with a newfound sense of adventure.
Perhaps she's a sister who was thought to be dead but actually survived. She could have been corrupted by the experiences she had while being 'dead'. When she returns, she blames Percy for not saving her properly. This false blame leads her to betray Percy. She could start spreading rumors about Percy being a coward or a bad leader among the demigod community.
Fanfiction.net is another good place. There are a lot of Percy Jackson - related fanfics there. Look for the specific category or use the search function to narrow down to the twin fanfictions. However, the quality may vary, so you might need to sift through some to find the really good ones.
A common theme is the discovery of the sister's powers. For example, she might find out she can control water like Percy but in a different way. This adds an interesting twist to the story as they learn to use their powers together.
I really like 'A Sister's Tale in the Percy Jackson Universe'. In this fanfiction, the sister character brings a new dynamic to the story. It shows how she copes with the knowledge of the Greek gods and her relationship with Percy, which is full of both love and typical sibling spats. It's a very engaging read.