One common theme is the integration of magic systems. Since Harry Potter has its own magic and the Olympian gods have their own powers, these fanfictions often find ways to blend them. Another theme is identity. Harry has to figure out his new identity as a god - like figure on top of being a wizard.
One popular 'Harry Potter is a god of olympus fanfiction' might be 'Harry Potter: Son of Poseidon'. In this fic, it combines the magical world of Harry Potter with the mythology of the Greek gods. It often has some really creative crossovers, like how Harry discovers his new powers related to being a son of a god.
Well, 'The Ascension of Harry' is a fanfiction where Harry becomes a god. This happens when he discovers an ancient magical artifact that grants him divine abilities and a new destiny.
Interaction might involve a bit of competition too. The demigods are used to physical combat and using their powers in a more direct way. The wizards, with their spells, might seem a bit sneaky to the demigods at first. However, they could learn from each other. A demigod could learn how to use a disarming spell, and a wizard could learn how to fight without relying on a wand from the demigods.
The meeting could also lead to some interesting cultural exchanges. The heroes of Olympus could introduce the concept of the Greek pantheon to the Hogwarts students. In return, the Hogwarts students could show them how to play Quidditch. Hermione would probably be really interested in learning about the ancient Greek magic that the heroes of Olympus might know. And Annabeth would be eager to study the books in the Hogwarts library.
Maybe a plot where Harry is the son of a major Olympian god, and he is sent on a quest that combines elements of the wizarding world and the world of Greek mythology. He could be searching for a powerful artifact that has significance in both worlds, like a magical weapon that was once used by a hero in Greek mythology and also has the power to defeat dark wizards.
Perhaps it could be Thor from Norse mythology. Thor is the god of thunder. So, Harry could have the power to control lightning or storms. He would be a very formidable wizard with such powers. His Hogwarts years would be full of situations where he uses these thunder - related powers to solve problems or fight off enemies.
Yes, in some Harry Potter fanfictions, there might be the concept of a 'god of magic'. Authors often take creative liberties to introduce such powerful and otherworldly entities to add new layers of mystery and power dynamics to the wizarding world they're building upon the original Potterverse.
Since it's a fanfiction, the 'god' could be anyone. It might be an interpretation of an existing powerful wizard in the Harry Potter universe as a god - like being. For example, Albus Dumbledore is often seen as an extremely powerful and wise figure, and in this fanfiction, the author could have elevated him to a god - like status for the purpose of training Harry. Or it could be a completely new entity from the author's imagination, perhaps a deity from a different mythology that has been inserted into the Harry Potter world.
On the Hogwarts side, Hermione and Ron would surely be there. They could be quite bewildered by Harry's newfound connection to Olympus. And Dumbledore, he might have some knowledge about the connection between the two worlds and could guide Harry in some way. From the Olympus side, Athena could also be involved as she is the goddess of wisdom and might see potential in Harry.