These Atalskes Phaser Corporation phasers were a dual-fire modification, where the Atalskes III was a type-1 hand unit that was designed to be mated with a type-2 phaser's phaser pistol power-pack grip, with the combined unit referred to as the Atalskes phaser IV. A keypad for the unit's internal computer was located in the joint coupling the two components.
The Atalskes III was introduced to Starfleet on reference stardate 2/12, and slowly began replacing the older Sestra phaser I units. This was not the sole design used by Starfleet, as the Sestra phaser IB was later in use concurrently. (ST reference: Mr. Scott's Guide to the Enterprise)
Atalskes phasers were among the collection of weapons obtained by the warlord Karnas on planet Mordan IV. Many of Karnas's advanced weapons were obtained through a deal with Commander Mark Jameson in the early 24th century. (TNG episode: "Too Short a Season")
This phaser was created for the unrealized 1970s Star Trek: Phase II television series (TOS reference: Star Trek: Phase II), and ended up being used on the USS Enterprise in the movies TOS movie: The Motion Picture and The Wrath of Khan. The prop was replaced by different phasers in TOS movie: The Search for Spock, but it was brought out of retirement for an appearance aboard the Enterprise-C in "Yesterday's Enterprise", indicating that the model of phaser continued into the 24th century.
Interestingly, while the prop was designed to separate into two units, the hand phaser modification described here was never seen separated from the grip unit in any production or publication.