Paulson is a character encountered within the Mothership Zeta DLC. He was abducted during from the "Wild West" hundreds of years ago.
When the player releases Paulson and the others from Cryo Sleep, he angry claims that he will "kill every last one of those bastards". If the player listens to the Alien Captive Recording next to Paulson's Cryostasis tube, you can pass a Speech check or if you have the Black Widow, you can learn that his Wife and Son were also taken and that they were separated.
He carries a unique Scoped .44 Magnum, Paulson's Revolver. The Revolver has no scope on it. The only way the player can obtain it is if they loot it of his corpse, as the version he uses cannot be pick-pocketed or used by the player.
When the player completes the Mothership Zeta DLC, Paulson will leave the ship and won't be there if the player returns. It is unknown if he enters the Capital Wasteland or travels to some other place within the United States.