If Harry was raised by a Basilisk, his magic might be intertwined with the power of the Basilisk's stare. He could potentially use magic to mimic some of the effects of the stare, like petrifying or paralyzing opponents. However, this type of magic would be very dark and he would need to learn to control it and use it for good, if possible. His overall magical development would be quite different from the normal Hogwarts education, as he would have these unique powers based on his upbringing.
When raised by an Acromantula, his magic could be attuned to nature in a different way. He might be able to use magic related to the forest and spiders more easily. His magic could have a more primal feel to it, as he learned from a creature that is not part of the wizarding human society. He could also have a natural ability to sense danger in the forest, which could be an extension of his magical abilities.
His magic might be darker. The environment of Arkham Asylum is full of negative energy. So, it could taint his magic in some way, making it more aggressive or unpredictable.
Werewolves are also a popular dark creature in fanfiction. Writers may explore their relationships with other characters in more depth, like how they interact with Hogwarts students. For example, a werewolf character could be a misunderstood outcast trying to find his place.
The Acromantula. Harry could come across a young Acromantula that is different from the rest of its kind. Instead of being aggressive, it shows an interest in learning about the human world. Harry, being the kind - hearted person he is, decides to befriend it. He might even teach it some basic spells or communicate with it using Parseltongue.
His magic might be more aggressive. Growing up with the Dark Lord, he would be taught to use magic for more forceful and often cruel means. For instance, instead of using a simple Stunning Spell like in the original, he could be using more dangerous and unforgivable - like spells without hesitation.
One plot idea could be that Harry is raised by Dementors. He might grow up with a very different view on life and magic. Since Dementors feed on positive emotions, he could struggle to understand concepts like love and friendship in the same way as in the original story. Another could be if he was raised by a group of Acromantulas. He'd likely be more in tune with the Forbidden Forest and its secrets, and might have a natural ability to communicate with spiders, which would be a very strange and unique power compared to his normal Gryffindor traits.
It could be about Harry Potter having some sort of connection or role as the 'king' of dark creatures in a fan - created story. Maybe he discovers a hidden power within himself that gives him control over these usually feared beings.
In Harry Potter fanfiction, the Boggarts can be very interesting. Writers might create unique forms that the Boggarts can take, based on the fears of different characters. The Thestrals are also popular. Fanfics could explore their connection to death in more depth or have them play a more significant role in the wizarding world. Additionally, the Nundu is a dark creature that might be given more detailed descriptions in fanfiction, like its venom having even more deadly effects.
The Dementors are quite popular. Their ability to suck out happiness and their overall spooky nature make them fascinating to write about. Werewolves are also common, especially with the whole Remus Lupin storyline in the original books. And the Basilisk is often used in fanfiction, with its deadly stare and connection to Salazar Slytherin.
In fanfiction, dark creatures can be more sympathetic. For instance, a vampire might be shown as a victim of his own condition rather than just a menacing figure. This gives readers a new perspective on these usually feared beings.
His friends would surely be affected. Hermione and Ron might be both amazed and a bit worried. They could be worried that this new power might change Harry too much or put him in more danger. Also, his enemies like Draco Malfoy would be affected. Draco might become more jealous or even more afraid of Harry.