Ianto Jones' father

Ianto Jones' father did not have a good relationship with his son. Ianto told his Torchwood team that his father enjoyed taking him to the cinema, (TV: From Out of the Rain) though his sister Rhiannon implied that their relationship was not as strong as he made out. Rhiannon and Ianto recounted that his father pushed him too hard on the swings in his childhood and broke his leg when Ianto fell off. (TV: Children of Earth: Day Two)

He was still alive in 2005, and would forcibly stay at Ianto's flat - an arrangement with which Ianto was not happy, as his father tended to break in if he could not find the key, pass out drunk, and wake up periodically to urinate on the carpet. Yvonne Hartman offered to retcon Ianto's family, purging their memories of Ianto's father, but Ianto eventually decided against it, saying his sister deserved to have a father. (AUDIO: Blind Summit)

In the last days of his life, he was hospitalised and waited three weeks for a call from his son, in vain, before he died. Ianto, dreading emotional upheaval at the thought this would without a doubt be the final time he spoke to his father, could not bring himself to say goodbye. (AUDIO: The House of the Dead)

Afterlife
Along with other dead people, he was "summoned" by the entity Syriath in the House of the Dead. He talked with a "revived" Ianto Jones, holding his "betrayal" against him. He tried to persuade him to let Syriath rise, in order to see again his passed loved ones such as his mother, Owen, Toshiko and Lisa. He disappeared along with every person "resurrected" by Syriath when Ianto sealed the Cardiff Space-Time Rift forever. It is unclear if this was the real Mr. Jones or an illusion crafted by Syriath. (AUDIO: The House of the Dead)

Behind the scenes
He was credited as "Mr Jones" in The House of the Dead. The full name of Ianto's father, however, has not been revealed.