Perhaps Kayla is the key to solving a major mystery in the Supernatural world. She might hold the knowledge or ability to defeat a powerful new villain that has emerged. This could lead to a series of adventures where she teams up with different characters from the show to uncover her true potential and save the day.
Kayla could be a fierce and independent character. Since she's related to Gabriel, she might have a similar sense of humor and a love for mischief. However, she could also be more empathetic and kind - hearted, using her powers to help those in need rather than just for pranks.
Gabriel's twin sister in the fanfiction could be a powerful force for good or evil. If she's good, she could be a key player in the fight against the demons and other dark forces. She might use her powers, which could include things like enhanced telepathy or the ability to teleport large groups of people, to help the hunters. On the other hand, if she turns out to be evil, she could be a new and formidable adversary. Maybe she was corrupted by the same forces that tried to use Gabriel, or she has her own reasons for going down a dark path. This would create a whole new dynamic in the Supernatural story.
One possible plot could be that Gabriel's twin sister has been hidden away by their family for some reason. When she finally emerges, she has powers that are different from Gabriel's but equally as strong. She teams up with the Winchesters to fight against a new, powerful enemy that is threatening the world.
You can start by looking on fanfiction websites like Archive of Our Own (AO3). It has a large collection of Supernatural fanfics, and you can use the search function to specifically look for stories about Gabriel's twin sister. Another option is FanFiction.net, which also has a wide variety of Supernatural - related fanfictions.
A great plot could involve her having a prophecy associated with her. The prophecy could state that she will either bring about the end of all supernatural chaos or be the cause of its ultimate destruction. This would put her in a very difficult position. Everyone in the Supernatural world, from the angels to the demons to the hunters, would be interested in her. Some would want to protect her to ensure the positive outcome of the prophecy, while others would want to kill her to prevent the negative one. Along the way, she would have to learn about her true nature and powers, and make choices that would determine the fate of the entire Supernatural realm.
One plot idea could be that Chuck's twin sister emerges from another dimension. She has different views on the story creation compared to Chuck. For example, she might want to save all the characters that Chuck has slated for destruction in his 'author' role. This could lead to an epic battle of wills between the two siblings over the fate of the Supernatural universe.
One unique idea could be a fanfiction where Gabriel teams up with Castiel to stop an apocalypse that was not part of the main Supernatural storyline. They could use their combined angelic powers in really creative ways. Another idea is a story where Gabriel gets trapped in a human body and has to learn how to live as a human while still having his angelic memories. This could lead to some really funny and heartwarming moments.
A fanfiction could involve Gabriel getting involved in the fight against Voldemort. He might use his trickster abilities to outwit Voldemort and his Death Eaters. For example, he could create illusions that confuse the enemy, which would give Harry and his allies an advantage in the battle.
Some fanfiction authors develop her by giving her a backstory that involves her being an outcast among the supernatural beings. Maybe she was shunned because of her relation to Lucifer. This then shapes her into a more empathetic character who wants to prove herself different from her twin. She might learn about human emotions and values, which further differentiates her from Lucifer, who has little regard for such things.
One idea could be that Tinkerbell's twin sister was turned into a vampire by a dark fairy's curse. She struggles between her new vampiric nature and her connection to the fairy world. Tinkerbell tries to find a way to break the curse.