Mix paprika, chili powder, onion powder, cayenne pepper, salt, and pepper together in a small bowl. Rub evenly over both sides of ribs. Place ribs, back-side down, on a wire rack.
Place rack in the preheated smoker. Add apple wood chips according to manufacturer's instructions. Smoke ribs until meat shrinks away from the bones, about 5 1/2 hours.
Remove ribs from smoker; cover with barbeque sauce. Wrap with aluminum foil. Let rest for 30 minutes.