A trident scanner was a 23rd century piece of Federation technology that was used for repairing power relays. (DS9: "Trials and Tribble-ations")
Spock used a trident scanner while he attempted to examine the circuits aboard the Galileo, after the shuttlecraft had been brought down to Gamma Canaris N. The scanner, however, was short-circuited and destroyed by the Companion when Spock attempted to make physical contact with it. (TOS: "Metamorphosis")
In 2267, Lieutenant Commander Montgomery Scott, leading a repair party aboard the USS Constellation, employed a trident scanner to cross-connect the warp drive control circuits to those of the impulse engines. (TOS: "The Doomsday Machine")
The same year, Ensign Harper used a trident scanner to connect the M-5 multitronic unit to the USS Enterprise's main power plant. He later attempted to disconnect M-5 with a trident scanner, but was vaporized by the advanced computer for his troubles. (TOS: "The Ultimate Computer")
Another model of the trident scanner was used on the bridge aboard the USS Enterprise-A while it was undergoing repairs in 2287. (Star Trek V: The Final Frontier)
In 2381, Ensign D'Vana Tendi found a trident scanner while cataloguing Kerner Hauze's collection. (LD: "Kayshon, His Eyes Open")