Yes, there are quite a few. You can find some on fanfiction.net. There are stories where Percy has to fight for his love in the context of the Percy Jackson universe, often facing various mythological threats while trying to protect his relationship.
One common theme is loyalty. Percy is already known for his loyalty in the original series, and in fanfictions about fighting for love, this loyalty extends to his romantic relationships. Another theme is sacrifice. He might have to sacrifice something important, like a personal goal or a powerful item, to protect his love.
In a fanfiction, the outcome could be whatever the writer wants it to be. If the writer wants to show Percy as an underdog who overcomes all odds, he could win. He might discover a new power or find a weakness in Gaea. For example, he could find that Gaea is vulnerable to a certain type of water, like water from a sacred spring. But if we look at their basic powers, Gaea is extremely powerful. She can create mountains and valleys with a thought. Percy would have to be extremely lucky and resourceful to defeat her.
Monsters from Greek mythology are also very common. Giants, like the ones Percy faced in the original series, are frequently used. They are powerful and require Percy to use his water - based powers in creative ways to take them down. It's a classic type of fight that fans love to read about.
One interesting Percy Jackson fighting fanfiction could be where Percy has to fight an ancient, forgotten monster that's resurfaced in modern times. Maybe it's a hybrid of multiple mythological beasts, and he has to use new strategies and his old skills to defeat it.
In Percy Jackson fanfiction, a relationship between Percy and Hestia could be really interesting. Hestia is the goddess of the hearth, representing home and warmth. A love story might involve Percy finding a new kind of peace and comfort in Hestia's presence. Maybe after all his adventures, he discovers a different kind of love with her, one that's more about stability and a sense of belonging.
Piper could also be a potential love interest in this scenario. Given her charm - speaking abilities, she could either be a rival to Percy in the 'player' game or be someone he tries to charm. Their interactions would be filled with a mix of friendly banter and underlying romantic tension.
In Percy Jackson fanfiction, the idea of Percy having a relationship with Demeter is quite an interesting concept. Demeter is the goddess of the harvest. A possible scenario could be that their love is based on Percy's respect for nature which Demeter represents. Maybe Percy helps Demeter in a quest related to protecting the harvest and in the process, they develop feelings for each other.
One great 'Percy Jackson' love fanfiction is 'The Sea's Embrace'. It beautifully weaves a love story between Percy and Annabeth in a post - war scenario. The author does an amazing job of showing their relationship evolving deeper.
In the Percy Jackson series, Gaea is a villain, and a love relationship between Percy and her in the context of the original story is very unlikely. However, in the world of fanfiction, anything can be created. There might be some fanfictions exploring such a strange and dark concept, but it would be a very unorthodox take on the characters.