Alright, so I saw a thread on tumblr ages ago that lives rent-free in my head now. The idea was that Percy is so used to all the weird monster goo and cleaning up after battles that he has this instinctive, hyper-efficient method for getting stains out of anything. The fanon joke is that Sally Jackson's greatest pride isn't her son saving the world, it's his preternatural skill with stain removal. He could probably get a decades-old wine stain out of white silk in under five minutes, and he'd do it while grumbling about how hydra blood is way stickier.
Then there's the whole 'Sally and Poseidon co-parenting group texts' scenario. The fans imagine Poseidon, this ancient deity, trying to use emojis and failing spectacularly. He'd send a simple 'How is our son?' and Sally would reply with a picture of Percy asleep on the couch, covered in glitter from some arts-and-crafts monster, and Poseidon would just respond with the volcano emoji because he thinks it means 'fiery spirit' or something. It's so dumb but I love how it makes the gods awkwardly mundane.
My personal favorite, though, is the idea that Percy's fatal flaw, personal loyalty, extends to inanimate objects. He gets weirdly attached to specific pens, or that one chipped blue mug at camp, and will fight anyone who tries to throw it out. Annabeth has to constantly stop him from bringing 'Riptide-adjacent' junk home, like a broken celestial bronze spoon he insists 'has potential.' It just fits his chaotic, sentimental energy perfectly.