There's one family I have been babysitting for for like, six or seven years now. There oldest son is great, their youngest son is alright, and their middle son is fucking weird in a very aggressive way, especially when I try to make him go to bed. It's rough. The most unsettling thing he does is like, I'll tell him it's time to go to bed, and he'll shriek. He'll shriek like his In pain. And it'll go on longer than it feels like it should, like his lungs shouldn't have that much air in them. And then he'll just walk upstairs as if nothing happened and stand in his room, which he shares with his brother, and I'll follow him up and he'll be like "shhhh! [Younger brother] is sleeping!" young know, as if he hadn't just shrieked so loud that younger brother is very much awake (and when he was younger it would usually make him cry too.) So I'll tell him to get in the bed and he refuses, he gets very angry and yells and hits the bed and throws things, but if I say anything he'll suddenly get very still and whisper "shhhh, don't wake up [brother.]"
And he claims he's afraid of the dark, even though he's fine in the dark in every other situation (I have to keep the doors locked and the keys on me at all times or else when I'm putting his brother down he'll sneak outside in the dark and just run through the big dark forest behind their house.) But his brothers can't sleep with the lights on, so I'll turn the lights off and he freaks out and goes in the closet and turns that light on, and he'll just bundle up in the corner of the closet and whisper to himself angrily in gibberish, and if I open the door he'll hiss and growl at me.
Overall he's just a very unsettling child and if someone told me he was possessed I would believe them.
Alternatively, a couple days ago I was babysitting for another family I babysit often for. Their daughter is on medication now because she had a lot of behavioral issues and it makes her kinda weird. They texted me at 6:30am asking if I could babysit at 7 and it was an emergency and they really needed me, so I said I could do it even though I had been drinking and only went to bed at like 5. So I was exhausted and a little drunk, and she wanted to play with her hamster on the couch so I sat on the couch and almost immediately fell asleep. I woke up only a couple minutes later but she was kneeling on my lap, staring intently at me. I asked her to get off and she didn't move, so I gently moved her off and she just stood there staring at me. I picked up the hamster and said we should out him back in the cage if she wasn't going to watch him, and she just stared at me. I moved to put the hamster away, had to go into the other room, but she didn't say anything or follow me, she didn't even turn her body from the couch, she just turned her head and stared at me while I put the hamster away. I went back to her and asked her if she was okay, no response, felt her forehead and she was okay, kept saying her name trying to get a response and she just kept staring right into my eyes, staring and staring... and then suddenly her dog ran past and she snapped out of it and ran after her dog, calling her name. I told her parents later and they said she jusy did that sometimes. It was incredibly unsettling.