One interesting headcanon could be about the backstories of the Servants. For example, there might be a headcanon that a certain Servant had a secret friendship in their past life that influenced their character in the game. Another could be related to the magic system in the Fate Grand Order universe, like a unique way of casting spells that isn't shown in the main story.
Well, a popular headcanon is that Percy can see the memories of the ocean. So in fanfiction, he might touch an old piece of coral and suddenly be flooded with images of ancient sea battles or long - lost civilizations. Also, some think that Annabeth has a fear of heights that she hides really well because she doesn't want to seem weak. As for Grover, perhaps he has a family of satyrs in a hidden grove that he secretly visits and they tell him old satyr tales that he then uses to his advantage on quests.
One popular Percy Jackson Percico fanfiction is 'The Sea's Embrace'. It delves deep into the relationship between Percy and Nico. The story has great character development and an engaging plot that keeps readers hooked. Another good one could be 'Under the Stars'. It shows their journey together in a unique and interesting way, with some really cool magical elements thrown in.
One great Percico time travel fanfiction is 'Time's Twist'. It has an interesting plot where Percy and Nico are sent back in time to the era of the Greek gods' early days. They have to navigate through various challenges while trying not to change history too much.
One great 'percico reading the books' fanfiction is 'Percico Library Adventures'. It has Percy and Nico exploring different magical books in a hidden library. Another one could be 'Percico and the Ancient Tomes', where they discover secrets within old books that are tied to their demigod world.
I like the headcanon where Annabeth is a master of disguise. In fanfiction, she can blend into any crowd, not just because of her intelligence but also because she has some magical items that help her change her appearance. It makes her even more resourceful on quests. Grover, on the other hand, has a headcanon where he can grow plants with just a touch. So if they're in a barren area, he can create a little oasis for them to rest in. This shows his connection to nature in a more powerful way.
One idea could be that Neville Longbottom is secretly a powerful wizard all along but has been suppressing his power due to self - doubt. Another could be that the Hogwarts portraits have their own little society and gossip network within the castle walls. And a third one might be that Hagrid has a secret family of magical creatures in the Forbidden Forest that he takes care of.
Well, it's the combination of two popular characters, Percy and Nico. Fans love to see how their relationship would develop in the context of time travel. They might be friends or more in different time periods, and exploring that is really appealing. Also, time travel gives the opportunity to bring in different mythologies and historical elements. For example, they could meet famous historical figures or mythological creatures from different eras, which makes the stories very rich and engaging.
You can try fanfiction websites like Archive of Our Own (AO3). It has a large collection of fanfictions, and you're likely to find 'percico reading the books' ones there. Another option is FanFiction.net.
It can add more depth to minor characters. For example, by creating headcanons about characters like Lavender Brown, we get to see a side of the Hogwarts student body that wasn't fully explored in the original. It gives them more personality and backstory.