One reason could be that Percy has shown great courage and strength, which Reyna respects. She might see in him the potential to be a great ally or even a leader. So, she becomes protective to ensure his safety and to keep him on their side.
It could also be that Percy has a certain naivete or innocence about him despite his powers. Reyna, having been through a lot, feels a sense of responsibility towards him. She may see a younger version of herself in Percy and wants to protect him from the harsh realities and dangers that she has already faced.
Maybe Percy has some kind of special power or ability that is crucial for their cause. Reyna, being a strategic thinker, realizes this and thus becomes protective of him. For example, if Percy has the power to control water and they are in a situation where water is a key element, she would want to keep him safe.
Another scenario might be when Percy is in a dangerous situation like facing a powerful monster. Reyna would not hesitate to put herself in harm's way to protect him. She might shield him with her own body or use her strategic mind to come up with a plan to keep Percy safe.
In one scenario, when Percy is about to face a powerful enemy alone, Reyna steps in and stands beside him, ready to fight together. This shows her protectiveness as she doesn't want Percy to take on the danger all by himself.
It can make some characters respect Reyna more. Since she is so protective of Percy, who is often seen as a hero, other characters may view her as a noble and loyal friend. For instance, those who look up to Percy would also appreciate Reyna for safeguarding him.
One reason could be that Percy is still deeply in love with Annabeth. His loyalty to her is unwavering, so he might reject Reyna out of his commitment to his existing relationship. For example, in the original series, Percy's relationship with Annabeth is built on years of shared adventures and mutual understanding.
It could also be due to jealousy. If there are rumors or a situation where it seems like Percy is getting more attention or praise than Reyna, especially in a military or leadership context. Reyna has worked hard to earn her position and respect, and she might not take kindly to Percy seemingly overshadowing her. For instance, if Percy is given a special mission that Reyna feels she should have been assigned instead.
Perhaps there are external factors at play. The world of demigods is full of chaos and danger. Reyna might be in a position where Percy feels he has to be by her side to protect her or to fulfill some greater prophecy that involves the two of them, and this leads to him leaving Annabeth.
Well, it could be simply due to a different kind of chemistry. Sometimes in fanfiction, the author wants to explore an alternative relationship dynamic. Reyna has a certain allure and mystery about her that might attract Percy. And the story could be set up in such a way that Percy and Reyna have more shared experiences at a particular point in time, which makes him lean towards her instead of Annabeth.
In a fanfiction, their friendship could start with a simple act of kindness. Percy could save Reyna from a minor accident. Reyna, being grateful, starts to see Percy in a different light. They begin to have small conversations, getting to know each other's likes and dislikes. Over time, they realize they have more in common than they thought. They support each other in their personal goals, like Percy helping Reyna with a project for the Roman camp and Reyna helping Percy with his relationships at Camp Half - Blood. This mutual support cements their friendship.
Maybe in the fanfiction, Percy and Reyna meet during a time of peace. They initially bond over their shared love for their respective camps. They decide to exchange knowledge, Percy teaching Reyna some of the more unorthodox combat techniques he learned from Poseidon, and Reyna teaching Percy about Roman military strategies. As they spend more time together, they also help each other deal with personal issues. Percy helps Reyna open up more about her feelings towards her sister, and Reyna helps Percy better understand his role as a hero in a changing world. Their friendship grows as they support and understand each other more deeply.
One possible plot could be that Percy is being controlled by some dark force. Maybe a new evil god or an ancient curse. This force makes him kidnap Reyna because she has some important knowledge or power that the dark side wants. For example, she might know the location of a powerful weapon that could tip the balance in a coming war between the gods and the titans' remnants. Percy, against his will, takes Reyna to a secret location. Reyna, being a strong and resourceful character, tries to figure out a way to break Percy out of the control while also dealing with the situation at hand.