Kryptonian Energy Pistols are weapons used by soldiers within Krypton's military.
Later on, when Lois Lane was released from her cell, Car-Vex came up with her weapon, only for Jor-El to shut the door, knocking the weapon out of the trooper's hand and telling Lois to pick it up. Jor-El also assisted in telling Lois where to shoot, while escorting her to an escape pod; however, the weapon was taken out of Lois's hand when she tried shooting on Car-Vex, who was attempting to stop the former's escape. Car-Vex did, however, manage to hit the escape pod with several shots, successfully damaging it as it launched from the Black Zero.
After the Black Zero Event in Metropolis, several Kryptonian weapons found their way onto the black market. Some criminals used these weapons including a Kryptonian pistol to break into Wayne Enterprises R&D Facility and steal from the vault. They were ultimately stopped by Superman who destroyed the weapons afterwards.
Kryptonian Energy Pistols are standard sidearm munitions designed to emit blue plasma bolts.