It's highly unlikely that the characters in 'House of the Dragon' would actually watch fanfiction about themselves. Fanfiction exists in our world, created by fans for fans, and the characters in the show are fictional entities within their own fictional universe. They don't have access to the fan - created stories about them.
A more complex idea could involve the magic systems of both worlds. The magic in 'Harry Potter' is more about spells and potions, while in 'House of the Dragon' there is magic that seems more in tune with nature and prophecy. A fanfiction could explore what would happen if these two magic systems collided. Maybe a Hogwarts professor tries to study the magic of Westeros and discovers new ways to use magic that were previously unknown in the wizarding world.
Definitely Daemon Targaryen. He's so mysterious and has this alluring, dangerous quality about him. Writers love to play with his character, creating different scenarios for him. Rhaenyra is also up there. As a central figure in the show, fanfiction often delves deeper into her emotions and her journey. Then there's Viserys. Some fanfictions explore his character more in - depth, especially his earlier days and the decisions he made that led to the events in the show.
One interesting storyline could be an alternate version of the Targaryen family's history. For example, what if a different heir was chosen? Another could be a story focused on the relationship between the dragons and their riders, exploring how they bond on a deeper level. And there might be fanfictions that focus on the politics of Westeros from the perspective of minor characters in the House of the Dragon universe.
Often, it's an ordinary person from our world who is reincarnated. They might be a big fan of the House of the Dragon in their previous life and now find themselves in this new, dangerous world.
Definitely not a true story. House of the Dragon is a work of imagination and creativity. It weaves a complex tale of power, politics, and dragons within a fictional realm.
Finally, when writing, try to blend the two styles of storytelling. 'Harry Potter' often has a sense of wonder and discovery, while 'House of the Dragon' has a lot of political intrigue and power struggles. Incorporate elements of both into your fanfiction. You can start with a small idea, like a dragon egg being found in Hogwarts, and then build on it, creating a story that is both engaging and true to the essence of both 'House of the Dragon' and 'Harry Potter'.
You can start by searching on popular fanfiction websites like Archive of Our Own. Just type in 'House of the Dragon' in the search bar and then look through the top - rated or most - reviewed fics. They are usually popular for a reason.
You could make an OC who is a dragon rider from a hidden dragon - riding clan. They enter the story during a time of great conflict, and their bond with their dragon is different from what is seen in the show. Their arrival could change the balance of power and the way people view dragons in the world of House of the Dragon.