Well, it could change a lot. For example, Percy might have different powers or a different status within the demigod world. Maybe he would be more respected or feared because of his relation to Poseidon. Also, his adventures might be more centered around the politics of the gods, as being Poseidon's brother would make him a more significant figure in their eyes.
Well, it would make Percy's relationship with Poseidon extremely complicated. Since Amphitrite is Poseidon's wife in Greek mythology, if she's Percy's mother, it means Poseidon has a different kind of connection to Percy. Percy might feel more conflicted about his fatherly figure. He could be in a strange position where he has to navigate between the relationship with his mother and the traditional view of Poseidon as a powerful and somewhat distant god - father figure.
It might make Percy more confident. With the trident, he has a powerful symbol of his father's support. He could use it to face stronger enemies and gain more respect in the demigod world.
If Percy lives with Poseidon in fanfiction, his relationship with the other demigods would be transformed. Some might envy him for his close connection to a major god. Others might look up to him even more as a leader. And those who were once his rivals might try to befriend him to get closer to Poseidon. At the same time, Percy would have to balance his new life with Poseidon and his loyalty to his friends at Camp Half - Blood, which could lead to some interesting character dynamics.
It can also make Percy more empathetic. Since he has such a powerful and protective father, he realizes the importance of protecting others too. He may be more likely to step in and help those in need, just as Poseidon does for him. This protection also gives Percy a sense of security that allows him to explore his own identity and powers more freely. He doesn't have to constantly worry about being alone or unprotected, so he can focus on growing as a hero and as a person.
Poseidon's comfort can make Percy more confident. For instance, if Poseidon tells Percy he has great potential, Percy will start to believe in himself more. This new - found confidence can lead to him taking on more challenges bravely.
Well, it completely flips the script. In the original, Percy has a different mom, and with Artemis as his mom, it would mean a whole new set of powers and relationships for Percy. He might be more in tune with the moon and hunting, and his connection to the other gods would shift. For example, his relationship with Apollo would be that of a nephew rather than just a demigod acquaintance.
In this fanfiction scenario, Poseidon's relationship with Percy would be full of twists and turns. At first, Poseidon might be shocked and a bit angry. How could his son be related to Leto? But as time goes on, he realizes that Percy is still his son and that this new connection could be used to their advantage. He starts to work with Percy more closely, guiding him on how to balance his powers from both Poseidon and Leto. They might have some father - son talks about the new responsibilities Percy has and how he can use his dual heritage to protect the world better. Poseidon could also start to see Percy as more of an equal, as he is now part of a more complex and powerful family tree.
His character could change in several ways. He would have a new sense of identity. No longer just a demigod with powers, but now something more 'aquatic'. He might be more curious about his father's world and want to spend more time there. This could lead to some conflict with his human side, as he has to balance his life on land and his new underwater existence. Also, he could become more of a leader among the sea creatures, as he has a unique connection to them through the tail.
In some versions, Poseidon might keep Percy's mother at a distance to protect her from the wrath of the other gods. He could send her gifts secretly to let her know that Percy is okay. For example, he might send a magical seashell that can communicate with Percy.
In some fanfiction, Poseidon's worry is shown through his direct actions. For example, he might send his messengers or minor sea deities to keep an eye on Percy. This shows that he is constantly concerned about Percy's well - being.