Well, it could be about her trying to redeem the name of her father. Maybe she joins the Holy Grail War not for power but to prove that Mordred's line can be heroic. She might form alliances with some of the traditional heroes, like Saber, and they initially have a lot of mistrust but over time come to respect each other.
Love and friendship are also common themes. An OC could develop a deep friendship or even fall in love with Mordred. This relationship can be complicated by Mordred's status as a Servant and the events of the Holy Grail War. It can also be a source of character development for both the OC and Mordred. For instance, Mordred might learn about different forms of love and loyalty through her relationship with the OC, while the OC might grow in courage and determination as they get closer to Mordred.
Yes, there are quite a few out there. Some focus on unique crossovers where the magic of Harry Potter's world combines with the lore of Fate Stay. For example, you might find ones where Mordred ends up at Hogwarts and has to adapt to the new magical environment. It's really interesting to see how different the two universes are and how the characters interact.
She would probably have a complex relationship with the Arthurian characters. For example, with Artoria, there would be a lot of tension. Artoria might see her as a reminder of Mordred's betrayal. But the OC could also try to show Artoria that she is her own person. With other Servants like Archer, she might be initially seen as an enemy, but if she shows her good intentions, they could become allies.
A plot could be that Mordred is summoned by a powerful ninja as a last - ditch effort to fight against an ancient evil that has emerged in the Naruto world. This evil has powers similar to some of the powerful Servants in Fate Stay Night, so Mordred's expertise is needed.
One reason is the character of Mordred itself. Mordred is a complex and interesting character in the Fate Stay Night universe. Fanfictions, especially lemon ones, allow fans to explore different aspects of the character in a more in - depth and sometimes more intimate way that might not be shown in the original work.
There are often fanfiction communities on Reddit as well. The r/fatestaynight subreddit might have some threads dedicated to OC and Mordred fanfiction. People often share their own works or recommend ones they've read. You can also look for Tumblr blogs that are focused on Fate Stay Night. Some bloggers are really into fanfiction and might have reblogged or written some interesting stories about OCs and Mordred.
One way could be to create a crossover universe where Mordred from Fate Stay Night somehow ends up in the Naruto world. Maybe she could be a new kind of ninja with her own unique abilities based on her Fate Stay Night powers. For example, her sword skills could be translated into a new form of kenjutsu in the Naruto world.
You can try some popular fanfiction websites like Archive of Our Own (AO3). There are a large number of Fate Stay Night fanfictions, including those related to Mordred. Just use the search function on the site and type in relevant keywords like 'Fate Stay Night Mordred' to narrow down the results.
A plot where Mordred attends Hogwarts undercover could be very interesting. She could be on a secret mission while trying to fit in with the students and learn about the wizarding magic, which is very different from her own powers.