Yes, you can put three cory catfish in a 10-gallon tank. As a general rule, a one-inch cory catfish requires one gallon of water in the tank. Depending on the species, an adult cory catfish can grow to be 2–4 inches long, so three cory catfish can live comfortably in a 10-gallon tank.
However, you should always try to keep your cory catfish in a larger tank. This is because cory catfish are schooling fish and thrive best in groups of at least six. Because a 10-gallon tank isn’t big enough for six corys, you should strive to keep them in a 20-gallon tank or bigger.