Are 1962 steel pennies counterfeits?

No 1962 US cents were struck in steel.

A genuine steel cent will stick strongly to a magnet. Most likely yours will stick weakly or not at all, which means it's a genuine bronze cent that's been plated with a silver-colored metal, probably for use in jewelry or as a high-school science experiment. In that case its value is only 1 cent because it's an altered coin.