You can put between two and four cory catfish in a 10-gallon tank. A one-inch cory catfish generally requires at least one gallon of water to live comfortably. Depending on the species, cory catfish can grow to be 2–4 inches long. Keep that in mind when considering your tank size and how many corys to bring home.
With that said, cory catfish shouldn’t really be kept in a 10-gallon tank. Cory catfish are schooling fish, and they thrive best in schools of six or more. For that reason, you should try to keep your corys in a 20-gallon tank or larger.