An electrical panel does put out EMF radiation but so does your electrical outlets in your room and anywhere else in your house.
The electrical panel puts out a bit more EMF radiation though than the electrical outlets making it more unsafe to sleep near the electrical panel.
I've slept near electrical panels before in rental homes where the electrical panel was inside the bedroom but nothing happened to me.
My bedroom as a kid was in a mobile home that also had the electrical panel in my bedroom and I'm still healthy today and never have gotten cancer.
I personally wouldn't worry about it though but if you're worried about it you can have the electrical panel moved away from your bed or move your bed into another bedroom away from the electrical panel.