He could be worshipped. If Percy is mistaken for a god, the mortals around him might start worshipping him. They would offer sacrifices and build temples in his honor. This would put Percy in a difficult position as he doesn't want to deceive people but also doesn't want to anger the real gods.
There could be a plot where Percy has to play along with being a god to achieve a certain goal. Maybe there's an evil force that can only be defeated if the people think he's a god. So he pretends to be one, using his powers sparingly to keep up the act. But as time goes on, it becomes harder for him to maintain the facade and he has to find a way to reveal the truth without causing panic or disappointment among the mortals who have come to rely on him as a god.
One possible fanfic could involve Percy being mistaken for Poseidon in a new underwater city. The residents see his powers over water and assume he's the sea god himself. He then has to deal with their expectations and demands while trying to explain that he's just a demigod.
Well, perhaps the archangel and Percy would have a power struggle at first. Percy is used to being in charge in his own adventures, and the archangel has its own set of divine powers and authority. They'd need to learn to work together, like when they encounter a group of mythical creatures that are causing havoc in both their domains.
Well, Percy could use his space powers to visit other planets. He might find demigods on other worlds or discover new mythologies.
He might gain new powers like controlling all aspects of water, not just the sea. He could also have the ability to create new sea creatures.
In a fanfic, Percy Jackson might face some really tough opponents in the contest. He could use his water - controlling powers in creative ways, like making a huge water barrier to protect himself from attacks. Maybe he'd also team up with some unexpected allies he meets during the contest.
In a fanfic where Percy Jackson becomes a god, he might gain new powers. For example, he could have more control over the elements, not just water. He could also have a greater influence on the demigod world. Maybe he'd be able to protect more of his friends and family from the various threats that constantly lurk in the Percy Jackson universe.
Poseidon is a likely candidate. Since he is Percy's father in the original series, it would make sense for him to take a more active role in raising Percy. He could teach Percy all about the ocean, its secrets, and how to use his water - related powers more effectively.
In this fanfic, Percy could be called upon to solve a mystery among the animals. Some animals are acting strangely and it seems like there's a curse. Percy uses his ability to understand the animals' language and his knowledge of magic to figure out the source of the problem. He might find out that an ancient artifact has been stolen and that's what's causing the chaos among the animals.
Well, he might gain new powers like the ability to control thunder like Thor. He could also have to deal with the Norse pantheon's politics. Maybe he'd form an alliance with Loki for some reason, who knows?
Well, Percy could meet Kratos. Maybe they'd fight at first because of some misunderstanding. Percy with his water powers and Kratos with his brute strength. Then they could realize they have a common enemy, like some new evil god trying to take over both their worlds.