Perhaps she is a time - traveler from the future. She has knowledge of future events that will endanger the ninja world and Sasuke. So, she tries to enlist his help, and in the process, a relationship develops between them. She might have unique abilities due to her time - traveling origin.
Perhaps it's a long - lost relative of one of the existing Order members. For example, a niece of Sirius Black who has just come into her magical powers and is eager to help the cause. She would bring a new dynamic with her connection to an established character.
She could be the daughter of a minor god that hasn't been introduced much in the original Percy Jackson series. For instance, the daughter of Hecate. This would give her powers related to magic, which would be really cool in the context of the story. She could use her magic to help Percy and his friends in battles or to solve some of the mysteries they encounter.
The new girl's character can be developed by giving her a unique backstory. Maybe she grew up in a different country and has a different style of martial arts. This would make her stand out and also influence her interactions with the other characters.
A character like a half - alien, half - human girl would be great. She could have the strength and some abilities from her alien side, but also the emotions and relatability of a human. This would make her a complex character with a lot of potential for growth and interesting interactions with the other Young Justice members.
The new girl Toa can be developed by giving her unique powers. For instance, if she has the power to communicate with nature in a way other Toa can't. Her relationships also play a big role. If she has a mentor, like an older, experienced Toa, she can learn from them and grow. This relationship can show her naivete at first and then her increasing wisdom as she trains.
There's a fanfiction called 'Friends Forever'. It focuses on the strong bond between the characters. The author does a wonderful job of showing how they support each other through thick and thin. It's full of heartwarming scenes and a bit of humor, just like the show.
One possible fanfiction could be about Jess getting pregnant unexpectedly. It could explore how the loft mates react. Schmidt might go into over - protective mode, while Nick could be initially shocked but then very supportive.
One idea could be that the new girl is a demigod from a very rare and powerful lineage. For example, she could be a descendant of a primordial god that no one has seen in centuries. This would bring a whole new dynamic to Camp Half - Blood as everyone tries to figure out her powers and where she fits in.
You can start by looking on fanfiction platforms like Archive of Our Own. Just search for 'New Girl Schmidt gay' and you'll likely find a variety of stories.