Probably Poseidon, as he is Percy's father and has a vested interest in his son's well - being. Zeus might also be protective in some cases, despite their past differences, as Percy is a hero who often saves the world which benefits Zeus's realm as well.
Their shared experiences play a big role. They've been through so much together, like countless battles and adventures. Percy has seen Annabeth in tough situations and he knows how strong she is, but also how vulnerable. So he feels the need to protect her. For instance, they might have had a close call in a previous adventure where Annabeth was nearly killed, and that memory makes Percy extra vigilant.
Perhaps Anko has a personal connection to Naruto. Maybe she sees a bit of herself in him, like his determination in the face of difficulties, and this makes her feel a sense of kinship and thus the need to protect him.
Well, it could be that in the fanfiction's plot, Harry has some special qualities or is in a dangerous situation. Edward, being a character with his own set of values, decides to be protective. For example, if Harry has some sort of power that others might want to misuse, Edward would step in to safeguard him. It might also be related to their shared experiences or a bond that has developed between them over the course of the story.
Maybe Blaise sees something special in Harry. In fanfiction, it could be that Blaise admires Harry's courage or his unique abilities. He might feel a sense of kinship with Harry despite their differences.
The word "father" may have different meanings in different novels, but it usually refers to the child's parent or guardian. In some novels, the father may refer to the biological father of the child, but in other novels, the father may refer to the adoptive father of the child or the role of the father in other relationships. Therefore, it was impossible to determine the specific meaning of a father in a particular novel. It had to be understood according to the context and plot.
Snape might be protective of Draco in fanfiction because in the original series, Snape has a certain loyalty to the Slytherin house. Draco is a young Slytherin, and Snape could see a bit of his own past self in Draco. Also, Snape was tasked with some difficult and dangerous missions by Voldemort. He might want to protect Draco from getting too deeply involved in Voldemort's dark plans to spare the boy from a similar fate as his own.