There have been various stories about children with mysterious powers from the Midwich Cuckoos to the movie The Ring.
I'm trying to recall a very specific short story. 1960s or earlier.
A young girl spends much of her time sitting in front of a TV. I can't remember whether the screen shows merely static or she somehow projects her own images onto the screen.
Adults (maybe her parents) are held prisoner by her and can't leave the house. It's possible that the girl has somehow separated the house from the normal world so that there is nowhere to go - there's just a grey mist outside. At some point she stops one of the adults from talking by sealing up their mouth - there is simply no mouth where it used to be and no scars or sign that it was ever there. I think she keeps them alive by using her powers.