Jeff Conniker, played by J. Alex Brinson, is the estranged father of Carly Shannon's baby, Jeffery Conniker Jr. He is an alcoholic who would often come home drunk and was abusive towards Carly. He also seems to stalk her while he's supposed to be on patrol.
History
He had been in a relationship with Carly sometime before the show started and they had a child, Jeffery, together. It's unclear if they lived together prior to Carly being overwritten by a traveler.
He was seen in the first episode. He'd come home after going out drinking. He gets angry at Carly because he thinks she's talking to her like he's an idiot and punches her, making her fall to the floor. He would have continued to beat her to death if Traveler 3465's consciousness hadn't have been overwritten. It's unknown what historically happened to him after he beat his girlfriend to death. Carly, now Traveler 3465, then asks him to leave which he does.
When he returns in the morning, Carly, now a traveler, tells him that she refuses to make up and that time spent with his son will now be one arranged hour per day and he needs to financially support them.
Jeff stalks Carly while he's supposed to be out on patrol and then confronts her on the street while she's out. He tries to beat her up on the street, though she's trained in hand-to-hand combat and ends up beating him. After she steals his car, he tracks it down to the abandoned building and manages to get trapped on the roof. (Travelers)
Traveler 5416
Traveler 5416 took over Jeff's body when Traveler 3465 forced a T.E.L.L. in which both 3465 and Jeff would have ended up shooting each other if Jeff had not been overwritten as per 3326's other timeline vision.
Traveler 5416 worked undercover in The Faction to rescue the Archivist A18 as The Director was blind to her whereabouts.
After helping A18 to the archive he is captured by 001 and questioned about Traveler 3569.
Traveler 001
During the time Traveler 5416 was captured he was overwritten by Traveler 001 before the team was able recused him.
During the events of Protocol Omega 001 fought with 3569 in David's apartment in order to get the code to take down The Director. When 3569 took her own life it forced 001 to leave Jeff's body and upload his mind into the Internet via Ilsa.