There are also fanfictions where James Potter wasn't really Harry's father. Instead, a mysterious and powerful wizard, hidden from the wizarding world, was his true father. This wizard could have been in hiding due to some dark prophecy or a powerful enemy, and his identity was kept secret to protect Harry from danger.
In some fanfictions, Sirius Black is sometimes portrayed as Harry Potter's real father. This idea might stem from Sirius's deep connection and loyalty to Harry, as well as his role as a father - like figure in Harry's life.
In some fanfictions, it could be Sirius Black. Some fans like to imagine that Sirius had a deeper connection to James Potter's family than just being best friends. They might create a scenario where there was some sort of magic or prophecy involved that made Sirius more than just Harry's godfather, but his actual father in this alternate story line.
Another possibility could be Draco Malfoy. Think about it. In some fanfictions, they might rewrite the relationships completely. Draco has his own complex character arc, and perhaps in this 'harry potter is not the father' scenario, he ends up being the father due to some unforeseen circumstances, like a misfired spell that alters the course of events related to parentage.
It could be one of Harry's enemies who is trying to frame him. So they set up the situation to make it seem like Harry is the father.
In this fanfiction, the 'Father of Monsters' might be an ancient wizard who has been in a deep slumber for centuries. He was awakened by some disturbance in the wizarding world and, feeling angry about the changes that have occurred, decides to create monsters to bring back what he believes was the 'true' order of the wizarding world. His knowledge of old magic gives him the ability to create extremely powerful and dangerous monsters that no one has ever seen before.
It could be Sirius Black. Maybe there was some misinformation that made Harry believe Sirius was his father for a while, but then it turns out he isn't. After all, Sirius was very close to Harry and had a father - like relationship with him in some ways.
Maybe Ron Weasley. Imagine a fanfiction where Ron, after getting married, has triplets. Given his humorous and sometimes clumsy nature, it would be really fun to see how he and his wife deal with three little ones. He could pass on his love for food and his loyalty to his children in a really endearing way.
It could be a pure - blood wizard from an old family in the Slytherin circle. Maybe someone like Theodore Nott. They could have been in a relationship that was kept quiet due to family politics or personal reasons.
It could be Ginny. In the original series, they had a relationship. An unexpected turn of events could lead to her being the mother in this fanfiction.
One possibility could be that Harry is the son of a powerful but mysterious wizard and a muggle - born witch who had to give him up for some reason. Maybe his real father was a dark wizard who was hunted down, and his mother was a brave witch who wanted to protect Harry from that dark legacy.
Apollo could be Harry's father. Apollo is the god of music, poetry, and prophecy among other things. If Harry was Apollo's son, he could have an innate talent for divination that is far beyond what he showed in the original books. He might also be able to use music as a form of magic, perhaps charming his enemies or healing his friends with melodies.