Defeat Maxson during the battle to get his weapon. The Railroad only path: either complete Precipice of War as described above, or carry on to the quest Rockets' Red Glare, which will have the Railroad attack the Prydwen. Play the Railroad quests until Precipice of War, and go to the Prydwen rather than the Police Station, and defeat Maxson there. The Minuteman path: you still need to join the Railroad as a Minuteman. Defeat him and loot the weapon from his body.

During the battle, you'll face Elder Maxson. The Gauss rifle is a coilgun, a type of projectile accelerator, which uses electromagnetic coils configured as a linear motor to accelerate ferromagnetic or conductive projectiles to extreme velocities. The Institute path: join the Institute after meeting Father and continue the questline normally until Airship Down. Gauss rifles are infantry fielded coilguns that appear in Fallout 2, Fallout 3, Fallout: New Vegas, Fallout 4, Fallout 76, Fallout Tactics, and Fallout Extreme. There are several ways to get this weapon, and in all cases you'll have to be hostile towards the Brotherhood of Steel. It's actually Arthur Maxson's personal weapon, and has a 25% increase in fire rate and 15% quicker reload time from a regular one. Final Judgment is an energy weapon, a classic Gatling laser which tends to be a popular choice for players specializing in energy weapon character builds.

Fallout 4 unique gauss rifle