Just bought a 62 Chevy Impala with a sbc 350. Gen light was on and battery was died and previous owner said the alternator was bad. Replace the battery and the alternator and the gen light is still on and the alternator is gettilng hot even with the car turned off. Any ideas.

Welcome to AF. Ign switches and related wiring were famous for overheating/burning out look at the connector on the switch, bottom of steering column, for discoloration. Then suspect a regulator problem, they are external of course.

From the factory, your car should have a generator (long & black). If someone changed it to an alternator (smaller with aluminum housing), something might be wrong with the conversion.

The hot "alternator" with the engine off is a sign of a ground problem somewhere, or a mechanical problem. Check your negative battery cable ground at the block, all the grounds on the firewall, make sure they aren't green and corroded. Loosen the fan belt and see if the "alternator" spins freely too.

Bob