There could be various interpretations of Percy's dream about his daughter Kelly in fanfiction. Maybe in the fanfic, this dream is a premonition of something important related to Kelly's future, like a special power she will develop or a great adventure she'll embark on.
Perhaps in the fanfiction, Percy dreams of Kelly in a perilous situation. This could then drive the plot as he tries to prevent this situation from becoming a reality in the real world of the story.
A less obvious but still present theme is the idea of legacy. Percy has a great legacy in the world of the stories, and his daughter has to deal with the expectations and responsibilities that come with being part of that legacy. This can add a lot of depth to the stories as she tries to make her own mark while living in her father's shadow.
One possible plot could be that in their dreams, they see their daughter growing up in a world where the threats they faced are no more. She is strong and confident, trained in the ways of the demigods. They dream of her making friends easily at Camp Half - Blood and having a special bond with the nature spirits there.
There's also a piece that focuses on Percy's dream daughter in a modern - day setting with a touch of mystery. In this fanfiction, the daughter discovers her true identity and has to deal with the challenges that come with being Percy's child. It's a great read if you like stories that blend the ordinary with the extraordinary.
They might become more protective. Since they are dreaming of having a daughter, they would start to think about all the potential dangers she could face. Their relationship could grow deeper as they bond over their shared hopes and fears for their future child.
Percy would use his combat skills. He has a lot of experience in fighting monsters, so if any threats come near his daughter, he'd be ready to fight them off with his sword. He'd also use his strategic thinking to outwit enemies.
She could be a completely new character created just for this fanfiction. Maybe she's a normal human girl who Percy discovers has a connection to the world of the gods in some way.
She could be the daughter of a minor god that has been forgotten or shunned. For example, the daughter of Hecate's lesser - known cousin who has some magic abilities but no real place in the demigod world until Percy takes her in.
Perhaps it's an old acquaintance from Percy's past who he reconnects with after leaving camp. They fall in love and she becomes the mother of his daughter.