In this fanfiction, perhaps Danny Phantom's identity gets exposed in his hometown in a way that makes it unsafe for him. Bruce Wayne, who is always on the lookout for those in need, decides to adopt Danny. Danny brings his unique perspective and powers into Bruce's world. He might start training with Bruce and the Bat - family, all while trying to keep his ghost - related problems from spilling over into Gotham's normal world.
Danny's powers could be a huge asset. His intangibility could help him and Batman get into places that are otherwise inaccessible. His flight would give them an edge in chasing villains across rooftops. Also, his ghostly energy blasts could be used as a new form of weapon against the bad guys in Gotham.
At first, it might be a bit rocky. Harry is used to the wizarding world and its ways, while Bruce has his own set of rules in Gotham. But over time, they'd start to understand each other. Harry would learn about justice in a different way from Bruce, and Bruce would come to respect Harry's magical abilities.
In this fanfiction, Bruce might see a lot of himself in Harry. Harry has endured great loss at a young age, just like Bruce. So, Bruce Wayne adopts Harry Potter. Harry could then grow up with access to both the wizarding world and Batman's resources. He could use his invisibility cloak in new and creative ways to help Batman fight crime in Gotham. And perhaps he'd introduce some magical elements to the Batcave.
The story might also focus on the relationship between Bruce and Percy. Bruce, having lost his parents, could see a bit of himself in Percy. He could become a father figure to Percy, guiding him and protecting him. Percy, on the other hand, could bring some light and a different perspective into Bruce's rather dark world. It could be a story of growth, both for Percy as he adapts to a new life with Bruce, and for Bruce as he takes on the role of a father - figure.
In a more emotional plot, Danny has lost his family in some ghost - related incident and is all alone. Batman, seeing a kindred spirit in Danny (both having experienced loss), decides to adopt him. Danny then has to adjust to living in the Batcave and being part of Batman's crime - fighting family. He struggles with fitting in at first but eventually finds his place and becomes an important asset to the team, using his powers in ways Batman hadn't thought of before.
Bruce Wayne is very brooding and serious, while Percy Jackson is more of a laid - back and sarcastic character. Their personalities could clash in the sense that Bruce might not always understand Percy's jokes or his more carefree attitude. However, they could also complement each other. Percy's light - heartedness could break through Bruce's dark mood sometimes.
One popular storyline could be Danny trying to adjust to a new life with Jason. Maybe he has to hide his ghost powers at first, which creates a lot of comical and tense situations. For example, he accidentally uses his powers in front of Jason's friends and has to come up with quick excuses.
His powers might also make Jason more protective. Knowing that Danny is different and has these abilities that could be exploited, Jason would be extra vigilant. This could lead to some arguments as Danny might feel smothered at times, but overall it would show how much Jason cares about him and is willing to go to great lengths to keep him out of harm's way.
His ghostly wail, a very powerful attack, could be used as a last - resort weapon against powerful foes in the Batman universe. However, it also might attract unwanted attention from other supernatural entities. Danny would have to learn to control it better in the more urban and populated Gotham. This would add an interesting dynamic to the crime - fighting in Gotham as they would have to deal with the potential consequences of using such a powerful ability.