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 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 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.
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.
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.
Well, it might start with Percy discovering his strange connection to Voldemort. There could be a lot of confusion and disbelief from Percy's side as he tries to understand how he could be related to such an evil wizard. And in the Harry Potter world, the characters would be equally shocked to find out about this new relation. It would be a story full of mystery and trying to figure out the how and why of this relationship.
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.
There might be. Fanfiction is a place for creativity to run wild. Imagine Percy Jackson suddenly showing up in the wizarding world where Voldemort rules. Percy's powers are not based on magic as Voldemort knows it. His ability to summon water in a place like Hogwarts could be a huge shock. Voldemort, who is used to being the most feared in his world, might be scared when faced with a being like Percy who has such different and potentially overwhelming powers.
It could be a very dark and complex story. Percy might be constantly at war with himself, having grown up in a more 'good' family environment but having this dark connection to Voldemort. He could be hunted by both sides - those who fear he'll turn out like his 'grandfather' and the remnants of Voldemort's followers who might want to use him for their own ends.
No. Percy Jackson's world is based on Greek mythology, while Voldemort is from the wizarding world of Harry Potter. Fanfictions might try to mash them up, but usually Percy has his own adventures and enemies in his own myth - based universe and is not related to Voldemort's heir. Unless a fanfic writer decides to do some wild crossover and come up with a really out - there reason for a connection.