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 be both terrified and intrigued. He's used to facing powerful monsters, but Cthulhu is on a whole different level. He might initially try to attack Cthulhu out of instinct, but quickly realize that his usual weapons and powers might not be enough. So he would likely retreat and try to come up with a more strategic plan.
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.
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.
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.
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.
Percy would probably be cautious. He's been through a lot with the Greek gods, and he knows how powerful divine beings can be. So, he'd approach this new encounter with wariness.
The characters' reactions would vary widely. Annabeth would likely be critical of any fanfiction that got the details of her character or her knowledge wrong. She's very intelligent and detail - oriented, so inaccuracies would bother her. On the other hand, if a fanfiction captured her essence well, she might secretly enjoy it. Leo would probably be excited to see all the creative ideas people had in fanfiction, especially if there were cool new inventions or adventures in them.