Yes, there are many great ones. You can start by looking on fanfiction websites like Archive of Our Own. Some focus on Percy's new adventures that draw on his unique heritage as the son of both Poseidon and Neptune, exploring how he might handle different mythological challenges.
One common theme is identity. Percy has to figure out how his dual parentage affects who he is. Another is power. Since he has two powerful godly parents, his abilities are often explored in different ways in fanfiction.
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.
One common theme is family. Since Percy is adopted by Hestia, the fanfictions often explore what it means to have a new family, especially in the context of the demigod world. Another theme is power. As Hestia has her own unique powers, Percy may inherit or develop related powers, which is a big part of many of these stories.
There are definitely some. However, the quantity might be less compared to more common pairings in the Percy Jackson fanfiction world. One great aspect of these fanfics is how they often blend the themes associated with Hades and Hestia. For instance, Percy might struggle with the duality of his nature - the brooding, dark side from Hades and the nurturing, home - like quality from Hestia. It makes for a very interesting read if you can find well - written ones.
Percy's powers would be more complex. He could have the ability to communicate with sea deities in a different way. Maybe he could use Hera's diplomatic skills to make deals with them or resolve disputes. His control over water could also be extended to other substances that have a connection to water, like steam or ice, in a more efficient way than before. And his powers of persuasion, which could be influenced by Hera, might be used to calm angry sea storms or make sea monsters cooperate with him, which is an interesting combination of his Poseidon - given powers and Hera - influenced skills.
One possible plot could be Percy struggling with the duality of his parentage. He might face discrimination from both the children of Hades and Poseidon. For example, the children of Poseidon could see him as a threat because of his connection to Hades, and vice versa. He could then go on a journey to prove that his dual heritage doesn't define him, but rather gives him unique powers to protect the world of the gods and mortals.
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.
One popular 'Percy Jackson adopted son of Hestia fanfiction' is 'The Hestia - Percy Bond' on Fanfiction.net. It has an interesting take on Percy's relationship with Hestia and how it changes his journey in the demigod world.
One way their romance could be portrayed in fanfiction is through Percy seeking solace in Hestia's hearth. Hestia, being the goddess of the hearth, represents warmth and home. Percy, having gone through so many harrowing adventures, might find a sense of peace with her. They could share quiet moments by the fire, with Hestia listening to Percy's tales of his quests. Their relationship could be a slow - burn one, starting from Percy's initial respect for her domain and growing into a deep, unspoken affection as he realizes how much her presence means to him in a chaotic world of gods and monsters.