Sorry, I can't really recommend specific 'Harry is related to the Queen' fanfiction as there are so many fanfiction platforms and it's hard to keep track of them all. But you can start by looking on popular fanfiction websites like Archive of Our Own and search for relevant tags.
Yes, there are likely some fanfictions out there exploring the relationship between Harry and the Queen in fictional scenarios. Fanfiction writers often take real - life figures and create unique storylines around them. However, the quality and nature of such fanfictions can vary greatly.
In fanfiction, one way Harry Potter could be related to the Queen might be through a magical alternate universe. Maybe the Queen is secretly a witch and has some connection to the wizarding world where Harry Potter exists. For example, she could be an ally to Dumbledore's side in the fight against Voldemort, providing resources or shelter to the Order of the Phoenix from her royal palaces which have been enchanted to be safe havens.
There could be fanfictions where the Queen has some sort of magical ability in the world of Harry Potter. For example, she might be a Squib who has a special connection to the wizarding world. In these stories, she could use her Muggle knowledge and influence to help the wizarding world in some way, like promoting peace between Muggles and wizards.
One great 'Harry Daphne Slytherin King and Queen fanfiction' is 'The Slytherin Royalty'. It beautifully weaves a story where Harry and Daphne take on the roles of king and queen in the Slytherin house. The story has great character development and interesting plot twists.
It might be an ancient magical being that has the form of a queen. She could have ties to the very origins of magic in the Harry Potter universe and decides to save Harry because she foresees his importance in the future of magic. For example, she could be a guardian of some sort of magic that is crucial for Harry to defeat Voldemort in the long run.
It could be an original character created specifically for the fanfiction. A young and beautiful queen of a small, yet prosperous kingdom, who has a strong will and a love for her people. She might be open - minded and curious about the wizarding world, which makes her a perfect match for Harry.
It could be the Queen of England, as in the real - world monarchy. In the fanfiction, she might be a figure with hidden knowledge of the wizarding world and decides to use her power to rescue Harry.
In this fanfiction, Harry Potter would interact with the Queen in a very unique way. Since he is used to the hierarchical system in Hogwarts, he would understand the importance of showing deference to the Queen. He could offer her a magical gift, like a charm that gives good luck. And the Queen, being curious, might ask him about his world. Harry would have to be careful not to reveal too much about the wizarding world to the muggles, but still satisfy her curiosity. There could be some misunderstandings too, for example, when Harry tries to explain some magic concepts using wizarding terms that the Queen doesn't understand.
There could be some of Harry's friends who might play a role. They could be the ones who encourage Harry to meet the Queen or who give him advice on how to behave in front of her.
One great 'fem Harry is a Queen fanfiction' could be 'Fem Harry's Queen Adventure'. In this story, fem Harry might discover Queen's music and it changes her life. She could start attending Queen concerts in the wizarding world, if there was such a concept. And she might be inspired by Freddie Mercury's flamboyant style to be more confident in herself.