There are quite a few. One popular one is 'The Time-Traveling Witch' where Hermione gets transported to the Doctor Who universe and has amazing adventures.
Well, 'The Magic of the TARDIS' is a well-known crossover. It combines the magical world of Harry Potter with the adventures of the Doctor in really interesting ways. The characters' interactions and the plot twists make it a great read.
Another great one could be those crossovers with the 'Lord of the Rings' universe. In these fanfictions, Harry Potter might find himself in Middle - earth, facing new challenges and making alliances with characters like Frodo or Gandalf. The contrast between the magic systems of both worlds makes for an interesting read.
I'm not sure specifically which ones are the most popular. However, you can start by looking on fanfiction platforms like Archive of Our Own. There, you can search for 'fem Harry Potter gets knotted' and browse through the results. Some might have high ratings and a large number of reviews which could indicate their popularity.
You might find fanfictions where Fem Harry has adventures with characters from Doctor Who or where her magical abilities interact with the Doctor's time-traveling escapades.
A well-liked one is 'Time and Magic'. It weaves a tale where Harry and Hermione's presence brings a unique dynamic to the Doctor's travels, facing challenges and uncovering mysteries together.
Fem Harry herself is often a very popular character in these fanfictions. Her new take on the traditional Harry Potter role brings a fresh perspective. Hermione also remains popular as she is often Fem Harry's closest friend and ally. Viktor Krum is also a popular character as his relationship with Fem Harry can be explored in new and interesting ways in the context of the Goblet of Fire story.
The novelty of the pairing. It's not a traditional pairing in the original series, so it offers a fresh perspective. Fans like to explore what - if scenarios.
These fanfictions are popular because they tap into the universal theme of betrayal. In the case of Fem Harry Potter, it's a beloved character put in a difficult situation. The betrayal can be used to explore complex relationships, such as friendships and loyalties. It also allows for a deeper exploration of the wizarding world's politics and power dynamics. For example, if she is betrayed by the Ministry of Magic, it can show the corrupt side of the magical government. This kind of storytelling makes readers think and feel more deeply, thus attracting a large audience.
One interesting 'Harry Potter is a doctor' fanfiction could be where he uses his magic in a new way to heal patients in the Muggle world. He might combine spells with modern medical knowledge. For example, he could use a spell to quickly diagnose an illness that normal Muggle doctors find difficult to detect.
One great Harry Potter crossover fanfiction is 'A Very Potter Musical' which combines the world of Harry Potter with a musical format. It has humorous takes on the characters and situations from the original series. Another one could be those crossovers with the 'Percy Jackson' series, where the magic of the two different mythologies interact in interesting ways. There are also some crossovers with 'Doctor Who' that take the TARDIS into the wizarding world and create unique adventures.