Do catfish produce milk for their young?

No. Catfish (order Siluriformes) are fish, and fish do not produce milk to feed their young. In general, catfish females lay eggs and those eggs are left alone. The hatched baby fish (called "fry") must fend for themselves.

They're called catfish because of the barbels that many species have extended from the sides of their mouths. They look sort of like a cat's whiskers. Catfish are bottom-feeders, and the barbels have taste buds in them that help the fish find food in the mud.