The implications are mainly negative. It promotes an unethical and immoral relationship that goes against basic human values. It can also be disturbing for readers who have a normal sense of right and wrong.
This is a rather disturbing concept as incestuous relationships are not acceptable in society. However, there might be some very dark and inappropriate fanfictions out there that explore such themes, but I would not recommend seeking them out as they go against moral and ethical norms.
I would highly discourage the search for such fanfiction. Fanfiction should generally be based on positive, ethical relationships. Incestuous themes can be very off - putting and can also violate the intended spirit of the original work's characters and relationships.
In some fanfictions, Percy's sister might hurt him emotionally by betraying his trust. For example, she could share his secrets with others, making him feel exposed and betrayed.
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.
Well, it could be because of jealousy. Maybe his sister gets more attention from their parents or is better at something that Percy wishes he was good at.
One way is through facing challenges together. For example, when they are on a quest, they might have to rely on each other's skills. Percy's sword - fighting skills and his sister's magic (if she has any) can complement each other. They also learn about each other's weaknesses and how to protect one another. In addition, they can have heart - to - heart conversations during quiet moments in their adventures, which will deepen their relationship.
One consequence could be a rift in the family. Their relationship might be so strained that it affects the whole family dynamic, causing tension during family gatherings or events.
One common theme could be family loyalty. Since they are siblings, many fanfictions might explore how they support and protect each other. Another theme could be growing up. They may face different challenges as they get older and fanfictions can show how they deal with those changes together.