Well, perhaps Percy could be teaching a new and difficult subject like Ancient Runes. He might use his strict and studious nature to get the students to really focus on the complex rune translations.
Hermione would likely be one of his favorites. She is extremely studious and always eager to learn, just like Percy. They could bond over their shared love for books and knowledge.
Well, it would be quite an interesting scenario. Percy Jackson is a demigod with his own set of skills and experiences. Teaching Defense Against the Dark Arts at Hogwarts would mean he'd bring a whole new perspective. He could teach students how to fight off monsters using his sword - Riptide, which is a very different approach from the usual spells taught at Hogwarts. His knowledge of Greek mythology might also come in handy when dealing with dark creatures that have their roots in ancient myths.
Maybe Percy teaches Potions. He could start off by strictly following the textbook but then discovers a new potion ingredient while exploring the Hogwarts grounds. This discovery could lead to a whole new line of potions research in the fanfic. He would then involve the students in this exciting discovery, making potions class much more interesting than it was before.
Percy himself is the central figure. But we could also have some of his old friends or siblings make an appearance. Maybe Fred and George could visit Hogwarts and play some pranks on Percy in his classroom, adding some humor to the fanfic. And then there could be a new transfer student from a foreign wizarding school who Percy has to guide in adjusting to Hogwarts life.
One spell she could teach is a charm for protecting books from any kind of damage. Given Hermione's love for books, this would be a great addition to the curriculum. Also, a spell for magically highlighting important parts of textbooks as you read them would be very useful. This spell could be activated by just thinking about the relevant information while reading.
Perhaps the story could revolve around them facing challenges within the Hogwarts faculty. There could be some old - fashioned professors who oppose their modern teaching methods. Harry and Hermione then have to prove that their ways are beneficial for the students. They might also discover new magical abilities in some of the students that were previously overlooked, and help those students develop their skills.
Perhaps Harry is teaching Potions in the fanfiction. Since he had a bit of a rocky start with Potions in his student days, he could be a very understanding teacher. He might encourage students to experiment more, which is different from Snape's strict methods. He could also share stories about how important Potions were in his adventures, like when they made Polyjuice Potion. This would make the class more interesting and inspire students to take Potions more seriously.
Well, perhaps Harry Dresden could introduce his unique brand of magic from his own world into Hogwarts. He might teach the students new ways of dealing with magical creatures that are different from the traditional Hogwarts methods.
One possibility is that Merlin brings his ancient magic knowledge. He might introduce spells and magical concepts long forgotten in the Hogwarts curriculum. For example, he could teach students about pre - Hogwarts era potion - making techniques that are more in tune with nature.