One possible plotline could be in a story that focuses on the family aspect of the demigods. If a female demigod has a child, breastfeeding could be a small part of showing the nurturing side of motherhood in the dangerous world of demigods. But this would have to be very carefully written to not overshadow the main themes of the 'Percy Jackson' world.
One possible plotline could be that an enemy tries to seduce Percy to turn him against his friends. This would create a lot of internal conflict for Percy as he has to fight against the charm or allure of the seducer while staying true to his comrades.
There is likely very little if any appropriate fanfiction on this topic. 'Percy Jackson' is mainly a series about adventure, friendship, and mythology. Breastfeeding is not a central theme in the original work, and creating such fanfiction might be considered strange or inappropriate by many in the fandom.
One way is by making him a new member of the Hunt. He could bring his unique skills like sword fighting and water control to help the Hunt achieve their goals. Another way is that he could be a reluctant ally, initially not wanting to be involved but getting drawn in due to some common threat.
One possible plotline could be Percy having to fight against other champions of different deities who see him as a threat. Another is that he has to find a way to combine his new role with his loyalty to his friends and the Olympians. For instance, he may be forced to make a choice between following Pontus' orders that might seem harsh to his friends or standing by his friends and risking the wrath of Pontus.
A possible plotline could be Percy seeing the movie and getting into an argument with another camper about whether Hercules' deeds were more impressive than his own. They could start listing their respective adventures and how they overcame challenges, leading to a friendly competition within the camp.
A possible plotline could be that Loki, being his mischievous self, accidentally gets transported to the world of Percy Jackson. Percy at first is suspicious but then realizes Loki can be an ally. They join forces to stop a powerful dark force that threatens both their worlds. Maybe this dark force is a combination of Greek and Norse mythological evils that only their combined powers can defeat.
In this fanfiction, there could be a plotline where Percy is initially confused and scared about being the father of Chaos. He then embarks on a journey to find out more about his new role. Along the way, he meets various characters who either help him or try to stop him. There could be a power struggle within the world of the gods as some see Percy's new position as a threat to their own power. Percy also has to deal with the moral implications of being associated with Chaos, whether to use its power for good or be consumed by it, and this internal struggle could form a major part of the plot.
Well, in a fanfiction, a plotline could be that Percy Jackson is on a quest and somehow crosses paths with Voldemort. Voldemort senses Percy's power and wants to study it. Percy, not knowing much about the wizarding world, initially mistakes Voldemort for just another monster. As they interact more, they realize that their worlds are more intertwined than they thought. Another plot could involve a powerful artifact that both of them are after. The artifact has the power to change the balance of both their worlds. So they are in a race against each other to get it, but along the way, they start to understand each other's motives and might even consider working together to keep the artifact out of the wrong hands.
One possible plotline could be that Chuchi somehow ends up in the Percy Jackson universe. Maybe she has a mission there and Percy helps her out. And during the process, they develop a special bond.
Perhaps Annabeth is wrongly accused of a crime and is made a slave as punishment. Her friends, including Percy, try to prove her innocence while also dealing with the internal politics of the demigod society that allows such a cruel situation to exist. This could involve a lot of character development for all involved as they question the fairness of their world's laws and norms.