One interesting story could be about Jason Blood's OC interacting with the traditional characters in the DC universe. Maybe the OC has a unique power that helps in a battle against a powerful villain. For example, if the OC can manipulate time in a small area, it could change the outcome of a fight with Etrigan.
First, think about the character of your OC. Decide on their personality, powers, and backstory. For example, if your OC is a shy but powerful mage, you can build their story around how they overcome their shyness to use their powers.
One possible scenario could be that Jason is in a state of shock. He might be thinking about how this injury could affect his role in the mission. He could be worried about letting his friends down, especially since he's always seen as a strong leader. 'I can't believe this happened. How will I be able to fight like this?' he might be thinking as he looks at his injury.
Love and romance can also be a theme. Some fanfictions explore a romantic relationship between Jason and the OC. This could involve the OC being a new arrival at Camp Half - Blood and catching Jason's eye, or they might have a pre - existing connection that develops into love over time. However, these stories also often balance the romance with the action and adventure elements typical of the Percy Jackson universe.
In Arkham Knight fanfiction, a Jason Todd OC might have unique abilities or a backstory that ties into the Arkham Knight's world. Maybe the OC has a connection to the criminal underworld in Gotham that Jason can use to his advantage in his fight against crime. It could also be that the OC is a scientist who helps Jason with some of the tech - related challenges he faces.
First, give the OC a unique backstory. Maybe they grew up in a family of hunters who were always on the lookout for supernatural threats like Jason. This would give them a certain set of skills and a reason to be in Jason's path. For example, they could be an expert in tracking and survival.
There are those where the OC is a meta - human with powers that somehow complement Jason Todd's skills. For example, an OC with the power of healing who helps Jason Todd recover from his more serious injuries and in the process, they develop a deep bond. In this type of fanfiction, the relationship between the OC and Jason Todd is often the central focus, exploring how they support and change each other.
Well, it could be really interesting. Jason Blood has his own set of powers and a rather complex personality. If he raised Harry Potter, Harry might grow up with a different understanding of magic. He could be exposed to more of the darker aspects of magic earlier, but also might gain some unique abilities or perspectives from Jason Blood's tutelage.
Fanfiction.net is also a good place. There are many authors who post their Jason Todd OC stories there. However, the site's interface might be a bit old - fashioned compared to AO3. But it still has a lot of great content if you take the time to search through it.