Typically, there are curious students. They are often in a learning environment, like a high school or college, and they accidentally stumble upon Percy and Annabeth's secret. They might be studying mythology and are really interested in finding out if the stories are real.
In some fanfictions, mortals might meet Percy and Annabeth in a coffee shop. Percy could accidentally use his powers to make a small water fountain out of a cup, and Annabeth would quickly cover it up while the mortals are left wondering what just happened.
Well, they might have to hide their demigod powers. For example, Percy could be really tempted to use his water - controlling abilities when they are near a big fountain in front of mortals, but he has to hold back. Annabeth would be using her wisdom to come up with quick lies if the mortals start asking too many questions about their strange behavior or the weapons they carry.
They interact cautiously. Since they are demigods and their world is full of secrets, they don't want to expose themselves. Percy might be a bit more laid - back in his interactions, cracking jokes with mortals while still being vigilant. Annabeth, on the other hand, is more calculating. She'll study the mortals first to see if they can be trusted.
Another option could be someone from a different mythology or realm. For example, an elf or a demigod from another pantheon. This would add an interesting twist to the fanfiction as it would bring in new elements and interactions between different mythologies and the mortals.
The fanfiction 'Mortals meet Annabeth's boyfriend' might have the mortals being really curious about their relationship. They could start asking all kinds of questions about how they met, what they like about each other. And perhaps Annabeth's boyfriend has to prove himself to the mortals in some way, like showing his strength or intelligence to gain their respect.
In a fanfiction, they might meet in a dangerous, enchanted forest. Percy has been lost in there for days, and Annabeth has come to find him. As Percy hears the rustling of leaves, he gets ready to fight, but then he sees Annabeth emerge from the bushes. Annabeth quickly assesses the situation and starts leading Percy out of the forest, all while they catch up on what has happened since they last saw each other. There are strange creatures lurking around, but they feel safer now that they are together.
They might lead normal lives, going to school, getting regular jobs. Maybe Percy would be a lifeguard at a local pool and Annabeth could be an architect student. Their relationship would lack the drama of demigod battles but would be filled with normal human challenges like dealing with family, exams, and making ends meet.
There could be a school janitor who is actually an old demigod who retired from the hero business. He could give Percy some valuable advice based on his own experiences. And of course, Percy will surely meet Annabeth's classmates, some of whom could be friendly and some not so much, depending on how they react to the new boy in school.
Grover could be one of Percy's friends to meet Annabeth. He's a satyr and has been with Percy through a lot. When he meets Annabeth, he might be really happy to see another important person in Percy's life.