One idea could be that she has unique magical abilities due to her demon - raised upbringing. For example, she might be able to communicate with dark creatures in a way normal wizards can't. Another could be that she struggles with her identity, being part of the wizarding world but also having this demonic influence. She could also face a lot of prejudice from the wizarding community who fear her because of where she was raised.
She could be a key figure in a war between the wizarding world and the demon realm. Since she was raised by demons, she might have some inside knowledge about their plans. However, she also has a connection to the wizarding world through her identity as Harry Potter. This could lead to a situation where she has to choose sides or try to broker peace between the two. Her magical powers could be a combination of traditional wizard magic and demon - like abilities, such as the ability to teleport short distances like some demons are thought to do in certain mythologies.
One plot idea could be that she grows up learning the unique magic and culture of the Delacour family. Maybe she has a special bond with Fleur and they train together for some wizarding tournament. Another idea is that she discovers secrets about her past that are different from the original Harry Potter story because of her upbringing by the Delacours.
One interesting plot idea could be that Snape, in raising Harry, teaches him advanced potions from a very young age. Harry becomes a prodigy in potions, much to the surprise of the other Hogwarts students. Another idea is that Snape's strict but fair upbringing makes Harry more reserved and less impulsive, which changes the way he interacts with his friends. He might be more cautious and calculating in his actions, especially when dealing with enemies like Voldemort.
One plot idea could be that Shield trains Harry in combat and espionage skills from a young age. This makes him a more physically and tactically adept wizard compared to the original story. He might use his new skills to uncover dark secrets within the wizarding world earlier.
One plot idea could be that Harry's grandparents are very strict about magic, so he has to secretly practice. Another could be that they are part of a secret wizarding society that has been in hiding, and Harry discovers their secrets. Or perhaps they have a special connection to Voldemort's past that Harry uncovers.
One plot idea could be that Harry discovers a hidden magic within the orphanage itself. Maybe there's a secret room that holds ancient spells or a connection to a long - forgotten wizarding family. Another idea is that the other orphans start to show signs of magic too, and Harry has to figure out how to protect them from the wrong kind of attention. Or perhaps the orphanage is under a curse, and Harry's presence there is the key to breaking it.
One interesting plot could be how Harry's magical abilities are perceived in a world of nations. Maybe he uses his magic to solve international disputes. Another idea is that different nations try to influence his upbringing, each adding their own cultural and magical elements to his training.
One idea could be that Harry grows up with cat - like reflexes and stealth. He might be able to move around Hogwarts unnoticed more easily, like a cat prowling in the shadows.
In the fanfiction, it could be interesting if Harry uses his magic to protect the other orphans from bullies. He might not fully understand his powers yet, but his instincts kick in. And then when he finally gets his Hogwarts letter, the other orphans are both sad to see him go but also excited for him, and he has to figure out how to leave the only home he's known while also being eager to enter the wizarding world.
One idea could be that Harry discovers his connection to the demons due to an ancient family secret. Maybe his ancestors made a pact long ago. Another could be that he has to use his new 'King of Demons' powers to fight a dark wizard who is trying to control the demon realm for evil purposes. He could also face challenges within the wizarding world as they fear his newfound powers.
One idea could be Harry being raised by the Weasleys from a very young age. He'd grow up with their large family dynamic, learning magic in a more chaotic but loving environment. It might change his personality a bit, making him more outgoing and confident earlier. Another plot could be him being raised by Remus Lupin. Lupin would instill in him a deep understanding of the dark arts in a more academic way, and also teach him about acceptance of his own lycanthropy - like condition if he were to inherit it. And a third idea is Harry being raised by the centaurs in the Forbidden Forest. He'd learn their unique brand of magic, which is more in tune with nature, and have a different perspective on the wizarding world and its relationship with the natural world.