Well, a possible storyline is Percy dealing with the expectations of the camps of Apollo and Athena. Since he's the son of both in this fanfiction, he might be pressured to be the best in both areas like archery and battle strategy. He could also go on a quest where he has to use his Apollo - given musical talent to charm a dangerous monster and then use Athena - taught wisdom to outwit another foe.
In this fanfiction, Percy would likely have powers related to both Apollo and Athena. Canon Percy has water - based powers from Poseidon. But here, he might have the ability to heal like Apollo, which would be a huge difference. He could also have enhanced intelligence and strategic thinking from Athena. So instead of just relying on his strength and water powers in battles, he could use his wits and healing abilities as well.
The Titans could still be a major threat. For example, Kronos' followers who might be trying to rise again and regain power. They could target the children of Athena because of their wisdom and strategic abilities, seeing them as a big obstacle to their plans.
Well, one possible plot could be Percy struggling to adapt to his new status as Apollo's adopted son. He might have to learn new powers related to the sun god. For example, he could start to have an affinity for healing, which is one of Apollo's main domains. And he would face challenges from other demigods who are jealous or suspicious of his newfound connection to a major god.
One interesting aspect of Percy, son of Apollo fanfiction could be his relationships. He might have unique interactions with other demigods. For example, his bond with those from different cabins could lead to exciting adventures. Maybe he teams up with a child of Athena to solve a mystery that involves both Apollo's powers of prophecy and Athena's wisdom.
Another plot could involve Percy having to prove himself to the children of Athena. Since he's not a child of Athena, they might be skeptical of his abilities at first. But as they face challenges together, like deciphering ancient prophecies that are hidden in Athena - related temples, Percy shows his worth through his quick thinking and battle skills. This could lead to a great friendship and mutual respect among them.
Percy would likely become more studious. Since Athena values knowledge, he would be more interested in learning about history, magic, and other aspects of the demigod world. He might spend more time in the library at Camp Half - Blood, much to the surprise of his friends. His relationships with others would also change. He could be more aloof at first as he tries to adapt to his new role, but as he grows into it, he would form deeper, more intellectual connections with those around him.
Another possible antagonist could be some of the more power - hungry and jealous demigods. They might not like that Percy has been adopted by Apollo and is getting special attention. They could try to sabotage his missions or spread rumors about him to turn the other demigods against him.
One great Percy Jackson and Athena fanfiction is 'Athena's Champion'. It really delves into the relationship between Percy and Athena in a unique way. The author portrays Athena as having a more hands - on role in Percy's adventures, guiding him with her wisdom in ways that are not explored in the original series.
One idea could be a story where Percy teams up with the Athena Hunters on a quest. Maybe they are searching for a lost artifact that has the power to change the balance between the gods. Percy's water powers could complement the skills and knowledge of the Athena Hunters.