In a 'Harry is the son of Hestia' fanfiction, the plot could be centered around the mystery of his true parentage. At first, Harry might be completely unaware of it. As he discovers the truth, he could face both acceptance and rejection from different quarters. His relationship with Dumbledore might change as Dumbledore tries to guide him through this new revelation. Also, his battles against Voldemort could take on a new dimension. Maybe Hestia's powers within Harry could be the key to defeating Voldemort in a completely different way than in the original series, for instance, by using the power of home and unity which Voldemort has always despised.
The plot could involve Harry learning about his true mother. Hestia, being a rather different kind of mother figure compared to Lily Potter. His relationship with other characters might change as a result. For example, he might have a different connection to the Gryffindor common room which is associated with the idea of home, since Hestia has ties to that concept. He could also have some new abilities or a different magical aura that sets him apart from the original Harry Potter story.
It could be about Naruto having powers related to Hestia. Maybe he inherits some kind of fire - based abilities from her. He might use these new powers to face tougher opponents in the Naruto universe.
In this fanfiction, perhaps Harry would inherit some of Hestia's qualities. Hestia is the goddess of the hearth, so Harry might have a strong sense of home and family. He could be a more nurturing figure, different from his canon self. His magic might also be influenced by Hestia's domain, like having an affinity for protective spells related to the home.
Yes, there are likely some fanfictions out there with this concept. You can start by checking popular fanfiction websites like Fanfiction.net or Archive of Our Own. Just search for 'Harry is the son of Hestia' in their search bars.
One plot idea could be Percy's struggle to fit in. Since his parentage is so unique, he might not be fully accepted by either the children of Hades or those of Hestia. Another could be his discovery of new powers. Maybe he can control both the underworld flames (associated with Hades) and the hearth flames (from Hestia).
In some fanfictions, there could be a plot where Harry, as the son of Hestia, has to face opposition from traditional wizarding families who don't accept this new 'parentage'. This would lead to him having to prove himself not only as a powerful wizard but also as a worthy heir to Hestia's legacy. He might have to use his wits and newfound powers to overcome these prejudices.
The plot could involve Percy being raised away from the typical demigod chaos under Hestia's care. He may be trained in the ways of maintaining harmony and peace. Hestia could use her powers to shield Percy from some of the more dangerous aspects of the demigod world, and in turn, Percy might become a sort of ambassador for her values among the other demigods, promoting the importance of a stable home environment and the bonds that come with it.
Obviously, Harry Potter himself is a main character. Since he is now the son of Hestia, his character development would be a central focus. He would be dealing with the implications of this new identity.
Perhaps Harry discovers his true parentage and has to deal with new powers related to Aphrodite, like charm and beauty - based abilities, while also trying to fit into the world he already knew.
One possible plot could be that Harry discovers his true heritage as Klaus' son. This could lead to a whole new set of powers and abilities for him, as well as a new family dynamic. Maybe he has to navigate the vampire world while still dealing with his wizarding roots. He could face challenges from both the wizarding community who are suspicious of his newfound vampire side, and the vampire world which might not fully accept him because of his wizard heritage.
Well, the plot could start with Harry finding out his true parentage. This would be a huge shock considering his normal 'muggle - born' or other normal origins in the original story. He might struggle with the new - found knowledge and the implications it has. Maybe he would have to deal with new powers that come with being Lucifer's son, and face opposition from both the wizarding world who see Lucifer as an evil entity and also from Lucifer's enemies in his own realm.