Epaphus was the son of Zeus and Io; his name, meaning "touch", shows the way he was born - that is, by Zeus' touch. He was born either on the island of Euboea, or in Egypt, on the river Nile. When he grew up, he became the king of Egypt. Moreover, he was considered to have been the founder of the city of Memphis, Egypt; his wife was also called Memphis and the two of them had a daughter, Libya.
Epaphus is also called Apis.