Percy would probably rely on his friends. In the Percy Jackson series, his friends were always there for him. In this fanfiction situation, he'd need them more than ever. They could help him stay grounded and remind him of his true self, not the dark legacy of Voldemort. Also, he might learn more about his demigod side to overpower the dark side in him.
Percy would first have to come to terms with this new aspect of his identity. It would be a huge shock, but he's a resilient character. He could study the magic of both the wizarding world and his demigod powers to find a way to co - exist with his new - found relation to Voldemort. He might also seek out wise beings from both worlds, like the centaurs in the demigod world or Dumbledore - like figures in the wizarding world. By understanding the nature of Voldemort's power and his own, he could find a way to use his powers for good and keep the dark side at bay.
In the fanfiction, perhaps Voldemort's grandson is not as evil as his grandfather. He could be trying to redeem his family's name. Percy Jackson might initially be suspicious of him but then they team up. The grandson could teach Percy some basic magic, and Percy could teach him how to be brave in the face of real danger, not just the kind wizards face. They might go on an adventure together to retrieve a powerful artifact that could change the fate of both their worlds. This would be a great way to explore the idea of good and evil not being so black and white.
One way could be to start with Percy discovering this strange connection. Maybe he has some strange dreams or visions that lead him to investigate. Then he could travel to the wizarding world to learn more about Voldemort. Along the way, he'd face opposition from both demigods who think he's getting too involved with dark magic and wizards who are wary of his demigod status.
One possible plot could be that Percy Jackson's grandson discovers a portal that leads to the wizarding world. He soon learns about Voldemort's reign of terror and decides to use his demigod powers to stop him. Along the way, he teams up with some young wizards and witches who are also against Voldemort.
Percy might be a bit curious too. He's used to strange things, and meeting someone related to such a powerful dark wizard could pique his interest. He could try to figure out if the grandson has the same evil intentions as Voldemort. He'd likely keep his distance at first, but as he observes the grandson, his reaction could change.
There might be very few fanfictions on this exact topic as it combines two very different fictional universes. But if it exists, it could explore how the powers from the Percy Jackson world, like the ability to control water or superhuman strength, would interact with the magic of the Harry Potter world where Voldemort resides. The grandson could be on a quest to stop Voldemort from getting some powerful demigod - related artifact that could enhance his dark magic.
In fanfiction, they could be related via a magical curse. A curse placed on Percy's family in the past by a dark wizard related to Voldemort could be the link. This curse could have some strange effects that tie their fates together. For example, Percy might be the only one who can break the curse and defeat Voldemort. Another way is if there is a secret magical society that both Percy and Voldemort are unknowingly part of, and the rules of this society create a relation between them, like they are both heirs to some powerful magic within the society.
It could be a wild mash - up. Percy might inherit some of Voldemort's dark magic tendencies while still having his own demigod powers. Maybe he'd struggle with the dark side of his heritage while trying to be a hero like he is in the Percy Jackson series.
He might try to understand the motivation behind it. Maybe he'd think that the author had some issues or was just exploring different ideas. He could approach it from an empathetic angle, but still be firm in his own self - identity and not let it affect him too much.
Well, in fanfiction, anything can be made possible. It could be a wild crossover where the author wants to explore the combination of the Percy Jackson and Harry Potter universes. Maybe some sort of magical mix - up or a prophecy that links Percy to Voldemort in a very strange way.
In the fanfiction world, the author could also give Percy some new powers or abilities specifically for this encounter. For example, he could have the power to nullify magic for a short time. This would be a huge advantage against Voldemort. Percy could then use his physical combat skills to overpower Voldemort and deliver the final blow. Another aspect could be that Percy's friends from Camp Half - Blood could help him in some way, like providing distractions while he goes in for the kill.