John Fitzgerald Archer was the presumed father of Sterling Archer, until it transpired by Dial M for Mother that his real father was unknown. Malory Archer concocted the story of Archer's father to protect him from the truth, as she admitted in the aforementioned episode. The backstory given by Malory was he was a Navy Cross-winning fighter ace pilot who was nicknamed Black Jack Archer and he died when Archer was little.
The name is an obvious reference to John Fitzgerald Kennedy, with the scene of Archer saluting at the funeral while standing next to his mother giving it away (it is a famous image of John F. Kennedy, Jr. from his father's funeral at 3). In reality, she had paid a Junior ROTC team in Yonkers $600 to give the 21 gun salute, which they used to travel to a competition in Albany and win third place. Like Archer's fictional father, Kennedy was in the Navy during WWII and had a distinguished career, receiving many medals, although not the Navy Cross. He served on a torpedo boat rather than being a pilot.