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.
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.
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.
Well, it could involve Percy having to adapt to a new family dynamic under Leto. He might learn new powers or abilities related to Leto's divine nature. Maybe he'd have to deal with Leto's other children, if any in this fanfic, and face new challenges that come with being part of her family.
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 interesting plot idea could be Percy having to team up with a demigod child of Leto. They could go on a quest to find a long - lost artifact that has the power to restore balance between the sea and the moon's influence. Since Percy is the son of Poseidon, his control over water and the other demigod's connection to Leto's lunar powers would create a unique dynamic.
Since Leto has her own history and experiences, Percy could become more empathetic towards the Titans. This newfound empathy could make him more diplomatic in his interactions with others. He might also become more of a loner, as Leto's adopted son, exploring the world on his own terms and trying to understand his new identity. This would shape his personality in a way that is both different from his original self and yet still retains some of his core traits like his sense of humor and determination.
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.
One interesting plot could be that Percy, while on one of his quests, stumbles upon a hidden place where Leto is in some kind of distress. Percy, being the hero he is, decides to help her. As they interact, they develop a mutual respect and a form of love that is more of a deep friendship kind of love. This love is tested as they face various mythological threats together.
When writing Percy, think about his backstory. He grew up knowing his divine heritage, which could have both positive and negative impacts. He might have been bullied by other demigods out of jealousy, so he has a bit of a guarded side. But he also has a strong sense of justice, inherited from Zeus, which makes him always ready to stand up for the weak. His relationship with his parents should also be explored. He could have a closer bond with Leto as she was more present in his life, while Zeus was often distant due to his many responsibilities in Olympus.