Well, perhaps Zatanna could use her magic to protect Harry from the Dursleys. She might teach him her unique brand of magic early on, which could give him an edge in the wizarding world. He could grow up learning both Zatanna's style of magic and the traditional Hogwarts magic, making him an even more powerful wizard.
One possibility is that Zatanna, with her skills in magic and illusion, could hide Harry in a different dimension or a magically concealed location. She'd raise him away from the prying eyes of Voldemort's followers. As he grows, she'd introduce him to the concept of good and evil magic, and how to use magic for the right reasons. This would shape Harry into a very different kind of hero compared to the one in the original series.
One possible plot could be that a magical accident or a powerful spell gone wrong transports Harry Potter to Zatanna's universe. They meet and initially have misunderstandings due to their different magical upbringings. But as they get to know each other, they discover that they share a common goal of protecting the innocent. Their relationship develops as they fight side by side against dark forces that threaten both their worlds, and eventually they fall in love and decide to get married.
One possible plot could be that Zatanna adopts Harry after she has a premonition about his importance in the fight against dark magic. She raises him in a world that combines the magic of the DC universe (where she's from) and the wizarding world of Harry Potter. Harry would learn to use a wand as well as some of Zatanna's signature magic tricks. When Voldemort resurfaces, Harry has not only the knowledge of Hogwarts magic but also the power of Zatanna's magic, which could include things like mind - reading spells and the ability to create illusions on a large scale, which gives him an advantage in the battle against the Dark Lord.
The plot could be that Harry, raised by demons, has unique powers that other wizards don't. For example, he might be able to communicate with dark creatures more easily. The demons could be using Harry as a tool to infiltrate the wizarding world. When he gets to Hogwarts, he starts to question his upbringing as he sees the kindness and different ways of magic there. He has to decide whether to stay true to his demon - raised self or embrace a new way of life.
One possible plot could be that Calypso, with her magical abilities, imparts a different kind of magic knowledge to Harry. Maybe she teaches him more nature - based magic, which is different from what he would learn at Hogwarts. Harry might grow up in a more isolated and peaceful environment with Calypso, away from the prying eyes of the wizarding world in Britain. This could lead to him having a different perspective on magic and his role in the fight against Voldemort.
The fanfiction might explore how Harry's relationship with the wizarding world is different. Growing up in Potter Manor, he could be seen as a more prominent figure from a young age. The manor itself could hold hidden chambers filled with challenges and rewards. Harry could stumble upon a chamber that tests his Potter lineage, like a series of magical trials. This would not only strengthen his magical abilities but also deepen his connection to his family name and the responsibilities that come with it.
One possibility could be that Harry Potter grows up with a strict military - like discipline on Kamino. He might be trained in unique combat skills that are different from what he learned at Hogwarts. He could also form unexpected alliances with the Kaminoans, and use their advanced cloning technology to his advantage in the wizarding world battles.
Perhaps the story could show Harry being isolated from the wizarding world he was meant to be a part of. Since demons are raising him, they might keep him away from Hogwarts and the positive influences there. He could develop powers that are a mix of wizardry and demonic abilities, which would make him a very different kind of character in the fanfiction universe. He might also have a different view on good and evil, as demons' moral compass is not the same as that of humans or wizards.
One possibility is that Harry would grow up to be a very different person. Dementors are creatures of despair, so he might be more withdrawn and less trusting. He could also have some very dark powers, having been exposed to the dementors' influence for so long.
Perhaps in this fanfiction, the goddess protects Harry from Voldemort right from the start. She could raise him in a hidden, magical realm where Voldemort can't reach. Harry would then grow up with a sense of security and a different kind of magical upbringing. He might learn to control his magic in ways that are more instinctual and natural, as influenced by the goddess.
The plot could involve Harry being trained in unique ninja skills by the Akatsuki members. He might learn their combat techniques and use them against the dark forces in the wizarding world. For example, he could use Akatsuki - style stealth to infiltrate Voldemort's lairs.