Yes, there are quite a few. You can start by looking on fanfiction websites like Archive of Our Own or FanFiction.net. Some might explore Percy's unique heritage as the son of both Gaea and Poseidon and how it affects his relationships with other characters in the Percy Jackson universe, like his friends at Camp Half - Blood or his enemies.
Well, a frequent theme is conflict. There's the internal conflict within Percy himself as he grapples with his dual heritage. Externally, there could be conflict with other characters who might view him differently due to his being the son of Gaea, a force that has been at odds with the demigods before. Also, themes of redemption can be present. Percy might feel the need to prove that he's not a threat like Gaea was, despite his connection to her.
This is a really interesting concept. In the original Percy Jackson series, Percy is the son of Poseidon. But in this fanfiction idea, if he were the son of Gaea and Tartarus, it would completely change his character and the story. His powers would likely be much darker and more primal. He might have an in - depth connection to the earth and the abyss, which could lead to some really unique storylines.
There's also a fanfic called 'Poseidon's Promise'. In this one, Percy has to deal with a mysterious prophecy related to his father. The story is full of twists and turns. It delves deeper into the relationship between Percy and Poseidon, which is really interesting to read about. It also has some great action scenes with Percy using his water - based powers.
One idea could be Percy feeling betrayed by Poseidon and then finding a new family among other outcasts in the demigod world. He could form a group with them and go on adventures that are not related to Poseidon at all.
In fanfiction, their relationship could be developed by having Poseidon be more involved in Percy's daily life. Instead of just popping in during big events, he could be there for the small things too. For instance, helping Percy with his schoolwork that involves marine biology. They could also have a project together like building a new safe haven for sea nymphs. Through this, they would bond over creating something positive. Also, Percy could start to take on some of Poseidon's responsibilities in the ocean, with Poseidon guiding him. This would not only strengthen their bond but also show Percy growing into his role as Poseidon's son.
Gaea herself would obviously be a main antagonist. She has the power to manipulate the earth and all its forces against Percy. Her children who are fully committed to her cause could also be major antagonists. They might have powers related to the earth and be very difficult for Percy to defeat.
One possible plot could be Percy's discovery of his true parentage. He might struggle with the implications of being the son of two powerful primordial deities. For example, he could face a conflict between the forces associated with Ouranos and Gaea. This could lead to him having to make difficult choices about which side to support, if any. And he may also have to deal with the reactions of his friends and the other demigods who might view him differently now.
One possible plot could be Percy discovering his true parentage as Gaea's eldest son and struggling with the implications. He might have to face the wrath of the other demigods who see Gaea as an enemy. For example, he could try to convince his friends like Annabeth that he is still on their side despite his newfound origin.
The plot could involve Percy's journey to discover the true meaning of being the son of Gaea and Pontus. He could be on a quest to find out more about his parents' realms and how they interact with the world of the demigods. Along the way, he may encounter mythical creatures that are related to Gaea and Pontus, and he has to either fight them or make peace with them. There could also be a sub - plot about Percy's relationships with his friends at Camp Half - Blood, as they struggle to accept this new side of him.