Yes, there are quite a few. You can start by looking on platforms like Archive of Our Own (AO3). There are some fanfictions that explore Percy's unique relationship with Tartarus in this adopted - son scenario. Some focus on his new powers, others on how he interacts with the other characters in the Percy Jackson universe with this new identity.
One interesting plot could be that Percy, being adopted by Tartarus, discovers secrets about his own past and his real parents that were hidden from him. Maybe his connection to Tartarus is not as random as it seems and it's all part of a much larger prophecy. This would involve a lot of mystery - solving, Percy going on a journey to uncover the truth, and him having to deal with the implications of what he finds out both in terms of his relationships and his own identity.
In most traditional Percy Jackson lore, he is the son of Poseidon. However, in fanfiction, authors can create all kinds of alternate universes. So, it's possible for him to be depicted as the son of Gaia and Tartarus in some fan - created stories.
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.
In this fanfiction, there might be a lot of focus on Percy's relationship with the other wolves in Lupa's pack. He could learn their ways of survival, their hierarchy, and how to be a part of their community. This would be a great way to explore his adaptability and growth.
Perhaps he could make an alliance with some of the less hostile creatures in Tartarus. There might be beings who are also tired of the chaos and want to help Percy in exchange for something, like a promise to free them from Tartarus if he ever gets the chance. Percy is known for his charisma and ability to make friends, even in the most unlikely situations.
Well, of course, Percy Jackson himself often makes an appearance. He could be a mentor figure to the adopted son, guiding him through the ropes of being a demigod. Annabeth is also common, perhaps helping the adopted son with her wisdom and knowledge of the mythological world.
The setting of the story might shift a bit. Instead of always being at Camp Half - Blood or on quests related to the Greek gods, Percy could be in the territory of the wolves. There could be new threats and challenges there, like rival wolf packs or ancient enemies of Lupa. And all these elements would make for an exciting and different take on the Percy Jackson universe.
If Percy was the son of Gaia and Tartarus in fanfiction, his power set would be a fascinating blend. From Gaia, he could potentially have the power of terraforming, reshaping the earth on a large scale. He might also be able to communicate with all forms of earth - bound life. From Tartarus, he could gain the ability to traverse the darkest depths of the underworld with ease, and perhaps even draw power from the primordial chaos there. This would make him a very different and much more complex character compared to his original form in the official series.
The fanfiction could also explore Percy's identity crisis. He's known himself as the son of Poseidon for so long, but now being the son of Gaea and Tartarus would shatter that identity. He would have to re - evaluate who he is, what his purpose is, and how he fits into the world of demigods. This internal struggle could be a major part of the story, with Percy constantly fighting against the darker impulses that come from his new parentage while also trying to find a place where he can be accepted and still be himself in some way.