Well, in many fanfictions, Percy is often shown as being physically protective. For example, he would jump in front of Annabeth if there was any danger, like facing a monster attack. He might also be verbally protective, not allowing others to say mean things about her.
Percy's protectiveness in fanfiction can manifest in him being over - cautious about Annabeth's participation in dangerous activities. He may try to persuade her not to take on certain risky tasks, even if she's determined. This is because he values her so much and can't bear the thought of losing her. He also shares his powers or resources with her to make sure she's always in a position to protect herself. For example, he might give her some of his underwater breathing ability - related items if they were in a water - related dangerous situation.
In some fanfictions, Percy's protectiveness of Annabeth can be seen in his constant worry about her safety. He would keep an eye on her during quests, even if she was fully capable herself. He might sacrifice his own comfort or convenience to ensure her well - being. For instance, he would give her the last bit of food or water if they were in a scarce situation. He also stands up for her in social situations, like when some demigods might be jealous of her intelligence and try to undermine her, Percy is right there to defend her honor.