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.
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.
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.
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 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.
Sirius Black is one of the most popular. His loyalty and his connection to Harry's family make him a natural choice. He has a wild side but also a deep love for Harry. Snape is also quite popular in this regard. Despite his complex relationship with Harry in the original series, in fanfiction, many explore the idea of him being a father figure, perhaps as a way to redeem his character. And of course, Hagrid. His gentle giant nature and his long - standing friendship with Harry give him the potential to be a great father figure.
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.
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.
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.
One potential character could be Seamus Finnigan. He has a bit of a fiery personality, and it would be interesting to see how he would handle being a teenage father. Maybe he accidentally gets into a situation where he has to take on this role.