His father has not been introduced. The anime suggests that his father was once a Pokémon Trainer who began his journey in Pallet Town, and that he is still living. In the original, he is also confirmed to have a grandfather, and his son (Ash's father) followed his footsteps. An interview with the series' storyboarder Masamitsu Hidaka confirmed Ash's father is a Trainer on his own journey. According to Hidaka, Ash's father may or may not be introduced in the series, depending on its necessity to further Ash's maturity and development as a Trainer.
Ash's father is unknown, and he may or may not be introduced.