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.
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.
One great 'Percy Jackson Ancient Greece Fanfiction' is 'The Lost Hero's Quest in Ancient Greece'. It has an exciting plot where the characters are plunged into a forgotten part of Ancient Greek mythology. The author does a wonderful job of weaving in the familiar elements from the Percy Jackson series with new and unique twists from Ancient Greek lore.
One common theme is time - travel. Since Percy is from a modern - day setting in the original series, sending him back to ancient Greece allows for all kinds of interesting scenarios. Another theme is the interaction with the Greek heroes and gods. Writers often explore how Percy would interact with the likes of Achilles or Apollo.
One common theme is the exploration of ancient Greek mythology. Since Percy is in Ancient Greece, there are a lot of opportunities to delve into the stories of the gods, heroes, and monsters.
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.
There's a good chance he'll meet the goddess Athena. Since Percy has a connection to the world of the gods, and Athena is known for her wisdom and strategic thinking, she could offer Percy some valuable advice. Maybe she'd help him navigate the complex social and political situations in ancient Greece or teach him some new ways to use his demigod powers.