One idea could be that Percy turns into a dragon to fight a powerful sea monster. Since he has his connection to water, as a dragon he could breathe a sort of water - based fire or ice that freezes the water around the monster, trapping it.
One possible plot could be Percy having to deal with new powers. He might struggle to control them at first, like accidentally causing thunderstorms when he's angry. Another plot could involve other characters' reactions. His friends might be in awe or a bit scared. For example, Annabeth could be worried about how this change will affect their relationship. Also, Percy could face new enemies who are jealous of his new god - like status or want to use his powers for their own evil plans.
His relationship with Annabeth would be really different. She would have to adjust to this new form of Percy. At first, she might be a bit scared or unsure, but then she would start to see the advantages of his dragon form and work with him. For example, she could use his ability to fly to reach places faster.
It could be an old enemy who now sees Percy as an even greater threat. Maybe Kronos' remnants. Since Percy is now a god, they might fear that he'll be able to fully destroy them. So they try to stop him from getting used to his powers or try to steal his powers.
One possibility could be that Percy, as a new god, would have to deal with the complex politics of Olympus. He's always been an outsider, and now he'd be thrust into a world of power plays and ancient rivalries. Maybe he'd try to change some of the archaic rules that the gods have held onto for centuries.
Perhaps Percy turns into a falcon. In this form, he could soar through the skies and spy on his enemies from above. He might use his falcon eyes to find a secret lair of a villain or to track the movements of the Titans. It would also give him a different perspective on the world around him, seeing things from a bird's - eye view.
In a 'Percy Jackson turns evil' fanfiction, he might use his powers against his former friends. For example, his control over water could be used to flood Camp Half - Blood. His knowledge of the demigod world would also be a weapon in his hands to outwit and defeat those who oppose him.
Well, in the fanfiction, if Percy turns into a baby, he would probably lose all his skills and knowledge at first. But he might still have some instinctual connection to water. Maybe his friends like Annabeth would have to take care of him. She'd be really protective and try to find a way to turn him back.
In the 'Percy Jackson turns into a cat' fanfiction, he could end up in some really interesting situations. For example, he might be chased by some of the magical creatures at Camp Half - Blood that don't recognize him as Percy. His senses would be heightened as a cat, so he could detect things like danger or hidden treasures more easily. Also, it would be hilarious to see how Annabeth reacts when she first sees Percy as a cat. She might be confused at first but then try to figure out how to turn him back.