Well, according to the Episode Guidelines:
In addition, by publishing your story, you agree that it does not include any content that infringes the intellectual property rights or rights of publicity or privacy of any third party. This may include using any of the following without permission:
- any works of authorship of other parties, including excerpts or passages taken from literary works, television or film;
- any trademarks or references to corporate or business names; or
- any references to real persons or places.
You can read more about the content guidelines for writing an Episode story here: Content Guidelines
You can’t have a story that features “fan-fiction” -this includes characters that already exist in a movie, book, etc. Having Percy Jackson in your story or any other characters & storytelling about Percy Jackson would go against the guidelines.
Anyways, good luck with everything!