Catfish do not have periods. Animals who have periods are placental mammals. They include primates, bats and elephant shrews. Catfish lay eggs that are externally fertilized.
Many types of catfish are cystovarian. This means their eggs are passed through the oviduct and continue to the outside and don't develop in a uterus. Catfish build nests on the bottom of a stream, lake or pond and deposit eggs or, like the stonecat, deposit eggs on the bottom sides of rocks. After the male fertilizes them, he may actually chase off the female and guard the eggs. In other species, both the male and female guard the eggs and fry.