Well, Percy's power over water is his most prominent one. In Hogwarts, there could be situations where the water in the plumbing system goes haywire due to some spell or curse. Percy could control it and prevent flooding. Also, in a big battle, he could create huge waves from any available water source to sweep away hordes of dark creatures. His demigod reflexes would be useful in dodging spells, and he could use his knowledge of Greek magic (if there's any connection in the fanfiction) to counter some of the dark magic being used against Hogwarts.
Percy's power over water could be used in potions class. He could manipulate water elements in the potions, perhaps making it easier to create certain water - based elixirs. Also, in Defense Against the Dark Arts, his combat skills as a demigod could be combined with defensive spells. For example, he could use his sword - fighting skills along with a Shield Charm to fend off attacks.
He might use his superhuman strength and speed, which he has as a demigod. With his enhanced physical abilities, he can easily take on many foes at once. And his power over water is a huge advantage. He could use water to create distractions or directly attack the villains.
Percy Jackson could protect Hogwarts by teaming up with the Hogwarts professors. He could offer his unique skills and knowledge. For instance, he could help in guarding the Forbidden Forest using his demigod senses. Also, his sword Riptide could be used to break through any dark magic - created barriers that the bad guys might set up around the school.
His water - controlling powers would make him an excellent teacher for spells related to water. He could demonstrate how to manipulate water in ways that normal wizards might not think of. For example, he could create huge water sculptures during class to teach about the properties of water in magic.
In this fanfiction scenario, Percy's adaptation to Hogwarts would be a complex process. He'd first have to deal with the cultural shock of a new magical world. The Hogwarts houses would be different from the cabins at Camp Half - Blood. He'd need to figure out which house he belongs in. His skills with a sword might not be as useful as in his own world, but he could learn to use magic to enhance his combat abilities. Also, he'd have to make new friends and enemies, and learn how to navigate the social politics of Hogwarts while still holding on to his own identity as a demigod.
One way it could work is that the spider powers could enhance his already existing skills. His reflexes, which are good from his demigod training, could be super - boosted by the spider - sense. And he could use his spider - like climbing ability to scale the walls of Mount Olympus or other mythical places that are otherwise hard to reach. This would give him an edge in battles against both mythical creatures and other demigods.
His water - controlling powers could turn the tides, literally. He could flood enemy trenches or create barriers of water to protect Allied troops. So, it could greatly affect the outcome by giving the Allies an edge in battles near water.
One possible new power for Percy Jackson in fanfiction might be the ability to communicate with all types of mythical creatures, not just those related to the sea. This would expand his network of allies and give him more knowledge about the mythical world.
Well, in fanfiction, Percy could have the power to control storms on a global scale. Imagine him summoning massive hurricanes to defeat his enemies or using gentle rain to heal the land. It would be a huge upgrade from his existing water - based powers.
If Percy had ice powers in fanfiction, it might also affect his relationships. His friends would see him in a new light, perhaps with a bit of awe or even some jealousy. He could use his ice powers for fun, like creating ice sculptures during downtime at Camp Half - Blood. This would add a new dimension to his character and the overall atmosphere of the story.