Some of the more malevolent spirits or monsters from the Underworld could also be antagonists. They might resent Percy for being Hades' adopted son and try to undermine him. For example, a powerful undead general who believes he should be the one favored by Hades instead of Percy.
One interesting plot twist could be Percy finding out he has a hidden power related to Hades' realm that he didn't know about before. Maybe he can control a special type of underworld creature that no one has ever seen. Another could be Percy having to face off against a false heir to Hades' throne who is trying to frame him for crimes in the underworld.
His relationship with Annabeth would become more complicated. She might be initially suspicious of Percy's new connection to Hades, but then come to accept it as part of who he is. Percy would also have a new dynamic with the other demigods. Some might fear him because of his link to the underworld, while others might be curious and want to learn more about his powers.
One idea could be Percy having to deal with the stigma of being associated with Hades in the demigod world. He might face distrust from other demigods who are scared of Hades' reputation.
Well, Percy might gain new powers related to the Underworld. Since Hades is the god of the Underworld, he could teach Percy how to control shadows or communicate with the dead. This would make Percy an even more formidable demigod, with abilities that no one else has. He could also face a lot of challenges from other gods who might be jealous or scared of his new connection to Hades.
His character would likely become more brooding. Being in the presence of Hades, who has a rather dark and serious nature, Percy might pick up some of those traits. He could be more introspective and less impulsive compared to when he was under Poseidon's influence.
One idea could be Percy having to mediate between Zeus and Hades during a major feud. Since he's the son of both in this fanfiction, he has a unique connection to them. He could use his powers and his knowledge of both of their domains to try and broker peace.
One common theme is the struggle with identity. Since Percy is usually the son of Poseidon in the original series, making him the Son of Hades in fanfiction often leads to him dealing with a new sense of self. Another theme is power and its consequences. Hades has a lot of dark and powerful abilities, so fanfictions might explore how Percy copes with having access to such powers.
One great 'Percy Son of Hades' fanfiction is 'The Underworld's Hero' on FanFiction.net. It has an interesting plot where Percy, as Hades' son, discovers new powers and faces challenges in a different light compared to the original series. The character development is really well - done.
Annabeth Chase might also be an ally. Her intelligence and strategic thinking could be valuable assets for the son of Hades. She could help him plan his moves, especially when dealing with the complex politics among the demigods and gods.