Yes, there are likely fanfictions with that concept available on various fanfiction websites. You can try searching on platforms like Archive of Our Own or FanFiction.net.
A fanfiction could also be centered around a magical artifact that links the two universes. Rhaegar and Harry Potter both get drawn to this artifact. They must work together to unlock its secrets. Rhaegar's knowledge of ancient magic and Harry's experience with the Dark Arts could complement each other in this quest, all while dealing with the political intrigue in both their worlds.
Yes, there are likely fanfictions out there with this concept. Fanfiction writers often create crossovers between different fictional universes like Harry Potter and Game of Thrones (where the Targaryens are from). You can search on popular fanfiction websites such as Archive of Our Own or FanFiction.net to find such stories.
One popular 'Harry is a Targaryen' fanfiction is 'Harry Potter and the Targaryen Legacy'. It combines the magical world of Harry Potter with the dragon - riding and complex family dynamics of the Targaryens in an interesting way.
The plot could involve Harry being born into the Targaryen family. He might be part of the fight for the Iron Throne. His magic from the Harry Potter world could give him an edge. He could also face challenges related to the Targaryen madness. His relationships with other characters like Daenerys would be interesting. Maybe he'd try to bring some of the more positive aspects of the wizarding world, like equality among different groups, to the feudal world of Westeros.
Perhaps in the fanfiction, Fem Harry Potter is a descendant of an ancient Targaryen who was sent to the world of Harry Potter for safety. When she returns to the world of Westeros, she meets Rhaegar. They could bond over their shared sense of duty. Rhaegar might be intrigued by her different kind of magic and her unique perspective on the world, and together they could work towards a more just Westeros.
One possible plotline could be their first encounter. Maybe Rhaegar, with his noble and somewhat mysterious air, meets Fem Harry in a forest. Their initial meeting might be filled with confusion as they come from different worlds but are drawn to each other's unique qualities.
Well, Harry might be initially cautious around Visenya. She has a very different and more aggressive style compared to his friends at Hogwarts. Visenya, on the other hand, could see Harry as someone with potential but also quite naive in some ways. Their interaction would be a clash of two very different cultures and ways of using magic.
Another interesting concept could be that Visenya is somehow transported to Hogwarts as a student. She has to adapt to the school rules and the different types of magic. She becomes friends with Harry Potter and they discover that there are some ancient connections between the magic of their two worlds. They might go on adventures in the Forbidden Forest, with Visenya using her Targaryen courage and Harry using his Gryffindor bravery.
Rhaegar Targaryen is often depicted as a noble and chivalrous character. He is known for his good looks and his skill in combat and leadership. He has a certain air of mystery around him, which makes him all the more appealing.