Well, perhaps Percy could find himself in a dimension where the laws of physics are completely different. He might have to learn new ways to use his powers. For example, if water behaves strangely there, like it's solid in some areas and gas in others, he'd have to adapt quickly.
He could also meet some sort of dark wizard or villain that is even more powerful than Voldemort in this new world. This would pose a great threat to Harry and force him to use all of his skills and knowledge, both from his own world and what he's learned in the new one, to defeat the enemy.
Well, in Harry Potter fanfiction, the 'Dimension Father' might be a character with a very specific role. Maybe he's a sort of guardian of the dimensional boundaries. He ensures that no dark magic from other dimensions seeps into the main Harry Potter universe. He could also be a source of knowledge for characters like Hermione who are always eager to learn new magic. For instance, he might teach her about the spells and incantations that are unique to other dimensions, which she could then use to help Harry in his fight against the dark forces.
Maybe it's a corrupted version of one of the gods from Percy's world who has gained even more power in this new dimension. They could be trying to spread chaos and destruction, and Percy has to stop them. This antagonist would know Percy's weaknesses from their time in the original world, which would make the conflict more intense.
Perhaps he'll come across a powerful wizard or witch who is the ruler of that dimension. This character could be either benevolent or malevolent, and would surely have a great impact on Harry's adventure in that dimension. They might try to use Harry for their own purposes or help him return to his own dimension.
In this kind of fanfiction, Harry might encounter new magical creatures that don't exist in his own dimension. For example, he could meet some kind of shape - shifting beasts that can change into any form they like.
Maybe he'll have to learn a whole new type of magic. In the other world, the rules of magic could be completely different. Instead of using wands, they might use their minds directly to cast spells. So Harry would have to adapt quickly to survive and figure out how to use this new magic system.
Well, he might make new friends. In a different school, there could be new magical traditions and spells for him to learn. He'd also face different challenges compared to Hogwarts.
In Harry Potter fanfiction, the dimension can be portrayed in various ways. Sometimes it's a parallel magical world with different rules. For example, a dimension where dark magic is the norm instead of being shunned. It can also be a place where time moves differently, like a dimension where a day in the regular Harry Potter world is a year there.