The Titan who fathered Atlas, Prometheus, and Epimetheus was Iapetus.
Iapetus was one of the twelve Titans, the children of Uranus and Gaia. He is usually paired with the Oceanid Clymene or, in another tradition, Asia. Their sons included Atlas, Prometheus, Epimetheus, and Menoetius, a family that links the Titan generation with several central myths about humanity and divine punishment.
Atlas was condemned to hold up the heavens after the Titanomachy. Prometheus became humanity’s benefactor after stealing fire from the gods, while Epimetheus—whose name suggests “afterthought”—accepted Pandora and her jar. Menoetius represented arrogance and violence and was struck down by Zeus.
The brothers are often treated as symbolic figures. Prometheus embodies forethought and clever planning; Epimetheus embodies hindsight and poor judgment. Their father is sometimes confused with Cronus or Hyperion because all three are Titans, but Greek genealogy distinguishes them clearly. Iapetus himself played a smaller role in surviving myths and was associated with the defeated Titans confined in Tartarus.