Mentally, she would be shaped by the Joker's insanity. The original Harry had a strong sense of justice and a desire to protect others. A female Harry raised by the Joker might not have such pure motives. She could be more self - centered, using her magic for her own amusement or gain. Her relationships would also be different. While Harry had close friends who shared his values, she might have more tenuous relationships, as she might not be as trustworthy or reliable due to the Joker's influence on her behavior and values.
She would be far more unpredictable. The original Harry was quite noble and adhered to a set of moral values. A female Harry raised by the Joker might not have such a clear - cut sense of right and wrong. She could be more likely to play pranks and use her magic in ways that are not strictly 'good'. For example, she might use magic to create chaos in a situation just for the fun of it, rather than to solve a problem in an orderly manner like the original Harry.
In the original Harry Potter story, Harry grows up in a somewhat ordinary (albeit cruel) Muggle household and then enters the wizarding world. In a 'Harry Potter raised by Catwoman' fanfiction, he'd be raised in a world full of crime - fighting (sort of) and stealth. His moral compass would be shaped by Catwoman's actions. He might not have the same friends as in the original story. For example, Hermione might not be as interested in befriending a street - smart Harry as she was in the book - smart Harry. His relationship with magic would be different too. He might use magic more as a tool for his Catwoman - inspired activities rather than for academic or traditional wizarding purposes.
Well, she would be much more hardened. The original Harry grew up in a relatively normal, albeit unloving, muggle household. But a female Harry in Arkham would have seen and experienced true horror and madness from a young age. So she'd be more cynical and less trusting.
Well, for starters, her moral compass would likely be more complex. The original Harry had a strong sense of right and wrong based on the values of the wizarding world. But a female Harry raised by demons might question those values more. She might be more cynical at first. For example, she may not see things like stealing magic items as completely wrong if she was taught by demons that survival is the most important thing.
She would likely have a different view of family. Growing up with the Delacours, she would have a more flamboyant and loving family environment. This would make her more confident in showing affection and relying on family support. In contrast, the original Harry had a rather lonely childhood until he discovered the wizarding world. Her relationships with others would also be different. She might be more diplomatic, having learned from the Delacour family's social skills, which could lead to different interactions with characters like Snape or Dumbledore.
The biggest difference would be his upbringing. In the original, he was raised by the Dursleys, which was a rather unhappy experience. With Sally Jackson, he'd have a more positive and nurturing environment. His view of magic would also be different. Instead of the somewhat formal and structured magic education at Hogwarts, he might have a more instinctive and hands - on approach influenced by Sally's parenting. And his friends would likely be different, perhaps including demigods.
The original Harry Potter story is set in a world full of wizards, witches, and magical creatures like dragons and unicorns. However, in a 'harry potter is a horse fanfiction', horses would take a more central role. There could be new storylines involving horse - racing in the wizarding world, or Harry Potter using his knowledge of horses to solve mysteries. Also, his relationships with other characters might be affected by his love for horses. For instance, some friends might not understand his newfound passion, while others might join him in his horse - related adventures.
Harry would likely be more wild in a sense. Dragons live by their instincts, and he'd pick up on that. His magical abilities could be more primal. Instead of relying on the spells taught in Hogwarts, he might use magic in a more raw and unrefined way. Also, his sense of loyalty might be more towards the dragons rather than the wizarding community initially.
His personality would probably be more aloof. Since basilisks are solitary creatures, Harry might not be as sociable as in the original story.
He would be more refined. Royal upbringing would instill in him a sense of propriety and elegance that he lacks in the original story.
In such a fanfiction scenario, Harry Potter's personality would likely be extremely distorted. The Joker's chaotic and immoral nature would probably make Harry grow up with a warped sense of right and wrong. He might be more prone to using cruel and unethical means to achieve his goals, far from the noble and kind - hearted Harry we know from the original series.