In 1942, after Johann Schmidt retrieved the Tesseract from Norway, Arnim Zola experimented on it and subsequently developed the weapon for HYDRA troops. During Captain America's Liberation of Allied Prisoners of War, several of these weapons were seized by the freed P.O.W.s and used against the prison guards.
In 2012, S.H.I.E.L.D. and the World Security Council launched a project known as Phase 2, in an attempt to create a Tesseract-powered weaponry, based on HYDRA schematics. Numerous assault rifles were stored at the Helicarrier where they were discovered by Steve Rogers, who then used it to condemn Nick Fury's secrecy.
The HYDRA assault rifle fires blue energy pulses that could vaporize humans. It was not as effective against other materials, but could still blast a hole in a brick wall in a barrage of shot. It was also useless against Captain America's Shield, as the pulses bounced off or were absorbed by the Vibranium.