Yes, there are quite a few interesting ones. You can start by looking on fanfiction platforms like Archive of Our Own. Some fanfics might explore Percy's relationship with his divine parents in unique ways, or perhaps put him in new and exciting adventures that are different from the original series.
Common themes include identity crisis. Percy has to figure out who he is now that his parentage has changed. There are also themes related to the Olympian hierarchy. With Zeus as his father, he might be thrust into a different position in the power structure. Additionally, themes of loyalty can come up. Who does he stay loyal to - his old friends and family or his new divine family? These themes make the fanfictions engaging and full of potential for complex storylines.
The Titans could be great antagonists. Since they often oppose the gods, they might see Percy as a threat, especially if he is the son of Leto. Kronos, for example, could try to stop Percy from fulfilling any prophecies related to Leto or the gods in general.
One idea could be Percy having to team up with Leto's other children in a quest to retrieve a powerful artifact that was stolen from their mother. Another could be Percy discovering a hidden connection between his powers and Leto's domain, leading to a new level of his abilities.
One possible plot could be Percy discovering his new parentage of being the son of Zeus and Hera. He might struggle with the new identity as it goes against what he previously knew. For example, he could face challenges from the other demigods who are suspicious or jealous of his new status. He then has to prove himself worthy of this new heritage while also dealing with the complex politics among the gods.
It could be a powerful Titan who escaped from Tartarus and wants revenge on Zeus by targeting his son Percy. This Titan might have unique powers that make him a formidable foe.
One common theme is identity. Since Percy is suddenly the son of Zeus, he has to figure out who he really is. Another theme is power. With Zeus as his father, he may have new and greater powers to control.
Some of the minor gods who feel overshadowed by Zeus and Hera might be antagonists. In this fanfiction, they could see Percy as a symbol of the over - dominance of Zeus and Hera. They might plot against Percy to send a message to his parents. These minor gods could use their unique powers and their knowledge of the magical world to create all sorts of problems for Percy, from cursing him to setting up traps in his path.
A powerful Titan who sees Percy as a threat to his plans. Since Percy has the power of Zeus and Poseidon, he could potentially stop any chaos the Titan wants to create. The Titan might try to turn Percy's friends against him or find a way to strip him of his powers.
A great plot could involve Percy discovering a hidden power within him due to his relation to Zeus. He then has to learn to control it while also dealing with the envy of other demigods. For example, he might accidentally cause some chaos in the camp which makes others suspicious and jealous of his new - found abilities.