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, 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")
The same year, 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")
Background information Edit
According to the final draft of the script for "Metamorphosis", dated 3 May 1967, this device was called "a ray-generator of some sort." The September 1968 Star Trek reference guide, The Making of Star Trek, described this device in production photos as a "(Spock built) ray generator and energy neutralizer."
The term "trident scanner," was described in the script for "Trials and Tribble-ations," where the device is apparently named after its general shape, which resembles a trident.