He could have adventures like battling mythical creatures. For example, fighting the Minotaur in the labyrinth. Maybe he'd also encounter the gods and goddesses and get involved in their power struggles.
His birth could introduce new prophecies. For example, the oracles might start predicting things related to Percy's fate that could change the course of events in Greek mythology.
If Percy Jackson was born in Greece, his story would be filled with even more direct connections to Greek mythology. He'd grow up surrounded by the ancient sites and stories. Maybe he'd be discovered earlier by the demigod community there. His powers could be more in tune with the original Greek magic, and he might have different relationships with the Greek gods who are closer to home, so to speak.
Well, in a fanfiction where Percy is born in Greece, his powers would likely have a more 'Greek - flavoured' aspect. Since he's in the homeland of the Greek gods, his connection to water could be intertwined with the Greek concept of the four elements. So, his water powers might interact more with the other elements in a way that is more in line with Greek elemental theory. He might also be able to draw on the power of Greek water deities more directly, which could enhance his abilities and give him new ways to use his powers in battles and other situations.
In some light novels, God's birth might be depicted as a result of cosmic forces or divine intervention. It could be a mysterious and awe-inspiring event.
In a fanfiction where Percy Jackson is born in Ancient Greece, his story could be intertwined with the great Greek heroes of that time. He could be trained by the likes of Chiron in a more traditional setting. His encounters with the gods might be more direct and less veiled as in the modern world. For example, Zeus might take a more immediate interest in him due to his potential power, and this could lead to a whole different set of challenges and quests for Percy.
He'd probably have a different set of enemies. In Ancient Greece, the threats might be more centered around the local myths and power struggles. For example, he could be in the middle of a feud between two powerful city - states, each with their own godly patrons.
His mother, Sally, would surely be one of his allies. She has always been there for him. Also, Grover could be his ally as they have a long - standing friendship. Grover might see Percy as an even greater protector of the nature spirits now that he's a god.
In ancient Greek mythology, the names of the 72 gods included Zeus, Hera, Hades, Persephone, Poseidon, Athena, Apollo, Artemis, Ares, Aphrodite, Hephaestus, Hestia, and so on.