How to treat ringworm on child's face?

Agree with Dr. M. If over the counter ointment for ring worm does not resolve the matter in a week or so, it would be prudent to see a doctor for a proper diagnosis.
Antifungal cream. Ringworm is not a worm at all, but a fungal infection, the same fungus that causes athletes foot and jock-itch. There are a number of antifungal creams that are safe to use on the face. Two tips, though. First, make sure to treat beyond the edge of the lesion - the fungus usually extends about a 1/2 inch past the edge. Second, be patient. It usually takes 4-6 weeks of continued use to clear up.