A phaser cannon was a type of directed energy cannon weapon, a powerful phaser bank, used by at least the United Federation of Planets, the Terran Rebellion, and Species 6339. It has been utilized as a ground vehicle mounted turret gun and an embedded starship-mounted weapon system. (DS9: "The Search, Part I", "Shattered Mirror"; VOY: "Infinite Regress"; Star Trek Nemesis; DIS: "Brother")
Ship-mounted phaser cannon
The starship-mounted Federation cannon was classified as an optronically targeted phaser. (VOY: "Live Fast and Prosper") Phaser cannons existed as early as the 23rd century, when the Crossfield-class starship USS Discovery was equipped with multiple phaser cannons. (DIS: "Brother") In the 24th century, they were part of the Defiant-class starship. (DS9: "The Search, Part I") In the mirror universe, the Defiant phaser cannons were called multi-targeting phaser banks by the Klingons. (DS9: "Shattered Mirror")
The four cannons of the Defiant-class were usually seen firing phaser bolts simultaneously in short rapid-fire bursts and in only one direction. The cannons could also fire beams. (DS9: "Destiny") Against Jem'Hadar fighters, the combined firepower of the four phaser cannons of the Defiant exceeded the firepower of two wing-mounted disruptor cannons of a Klingon Bird-of-Prey. (citation needed • edit)
On the Defiant-class, the plasma conduit was run through the primary phaser coupling to almost double the power of the phaser cannons. On most Federation ships, this would have significantly reduced warp drive efficiency. (DS9: "Defiant") Phaser safeties were engaged before the weapons array was brought on-line and the phaser cannons charged to full power. (DS9: "The Changing Face of Evil") When the cannons were charged, fifteen-percent plasma was bled to the phaser matrix. (DS9: "For the Uniform") There was also a separate phaser generator from the emitters. (DS9: "Starship Down") There were also phaser reserves that could be emptied, for example to strengthen structural integrity. (DS9: "The Sound of Her Voice") There was a thirty-inch-long power cell in the phaser array on the Defiant-class starships that was easily used up and needed to be replaced. (DS9: "Favor the Bold")
With extensive modifications, involving shunting the primary phaser relay through the warp drive, and bypassing the plasma emitter from the emitter coupling servos to avert an overload, phaser cannon array could be modified to emit a phaser beam wide enough to encompass an entire comet and vaporize it evenly from a distance of ten kilometers. (DS9: "Destiny")
In 2373, the throughput reading of the phaser relay on the Defiant was 148.7. Lieutenant Commander Worf and Ensign Nog attempted to increase the relay efficiency. This process involved recalibrating the emitter stage after the interface program was initialized and prefire chamber charged. (DS9: "Soldiers of the Empire")
Other species phaser cannons
Species 6339 utilized phaser cannon technology. One of their vessels, commanded by Ven, encountered by the USS Voyager in 2375, was found to possess twenty-two phaser cannons on the aft section alone. (VOY: "Infinite Regress")
Ground vehicle-mounted phaser cannon
Starfleet ground vehicles could be equipped with a personnel-operated phaser cannon. The Argo shuttlecraft, attached to the USS Enterprise-E, was equipped with a buggy which was armed with such a device. (Star Trek Nemesis)
- Optronic weapons array
- Phaser pulse
- Photon pulse
- Proximity blast
- Pulse cannon
- Tetryon pulse launcher
The use of the term "phaser cannon" was used on a computer screen in "Live Fast and Prosper" (used along with a cut-away graphic that first appeared in the Star Trek: Deep Space Nine Technical Manual, p. 133) and in dialogue in DIS: "Brother".
It was a common interpretation that the Federation phaser cannon was developed by Starfleet specifically as a weapon against Borg ships. According to "The Search, Part I", the Defiant-class was designed only for the one purpose, to fight and defeat the Borg, and, prior to the phaser cannons being referenced in the episode "Brother", it was often presumed that the first ship type to carry phaser cannons was the Defiant-class. (citation needed • edit)
The script of "Destiny" called the weapon a Gatling gun phaser.  There is, however, no evidence of any rotating barrels or emitters. On screen, in the dialogue, the Defiant cannons were always called simply "phaser banks" in such episodes as "Second Skin", etc., or just the "phaser array" in "Defiant". The four cannon simultaneous phaser volley of fifteen shots (sixty bolts total) was called "a standard burst" in "Destiny".
The term "phaser bolt" was used in the scripts of "For the Uniform"  and "Tears of the Prophets".  Visual effects have shown firing rates from four, in Star Trek: First Contact, to twelve rounds per second, in such episodes as "Valiant" and "Tears of the Prophets". Cannons have also been seen firing sequentially in pairs (first lower, then upper, ...) when the Defiant assaulted the last ships standing in its way in the Dominion fleet in "Sacrifice of Angels".
Although the impostors in VOY: "Live Fast and Prosper" displayed phaser cannons as a weapon system on the USS Voyager, there is no evidence that phaser cannons actually were part of the armaments of Voyager. The same graphic also appeared on Voyager's weapon manifest in the episode "Bliss", but was presumably intended as a generic weapon graphic.
The turret gun of the Argo buggy in Star Trek Nemesis was identified as a phaser cannon in the script of the film.  24th-century phaser rifles have also been shown to have a similar phaser bolt firing capability in "Worst Case Scenario", etc. Though not seen on screen, the user end of the phaser cannon contained a tactical LCARS display. This was shown in the It's A Wrap! sale and auction.  According to the apocryphal Starfleet Operations Manual, the tetryon pulse launcher, mentioned but not seen on screen in Star Trek: Insurrection, was a similar hand-held version of the phaser cannon.
In the first draft of the script of Star Trek: First Contact, the USS Enterprise-E was also intended to have port and starboard batteries of rapid-fire phasers resembling gatling guns in their effect. They were able to destroy a Borg cube before the Borg ships adapted their shields to the cannons. 
In the Star Trek: Deep Space Nine Technical Manual, the Defiant's phaser cannons are called "pulse phasers" or "pulse phaser cannons." The weapon combines several new technologies, such as nearly flawless emitter crystals, rapid discharge EPS capacitance banks and high-speed beam-focusing coils. The pulses are structured like a layered onion. As a result, the target contact is more difficult to disperse than a standard phaser beam. On the Defiant, the EPS weapon-power conduits have been truncated to provide a near-zero lagtime between activation command and beam launch. (pp. 123, 132, 133) Miranda-class starships were also armed with two pulse phaser cannons. (p. 154) Star Trek: Starship Spotter identifies the classification of the cannons as Type XII phasers.
In the script of Star Trek, when Captain Christopher Pike is recruiting James T. Kirk to join Starfleet, he comments on the cadets who fought with Kirk in the Shipyard Bar, that "they'll run home to momma the minute they're looking down the barrel of a Klingon phaser cannon." This suggests Klingons were using phaser cannons during the mid-23rd century of the alternate reality. 
The ships in Star Trek: Discovery have what appear to be phaser cannons; in a sense, they fire in a series of bursts. It isn't until Season 2 that the weapons take on their beam-like firing pattern with their signature sound effect.
According to the Pocket Books novelization The Search, by Diane Carey, the phaser cannon is called a triple-redundant interlocking phaser array. According to the novel A Sea of Troubles, the Miranda-class starship USS Samson (β) was upgraded with Defiant-class type pulse phasers. According to the novel Gods of Night, the Vesta-class (β) starships were armed with Mark XII phaser cannons.
The video game manual for Star Trek: Starfleet Command III describes the phaser cannon in great detail:
- "The Pulse Phaser is an advanced heavy weapon designed for a high rate of fire and a high damage yield… The Pulse Phaser was developed by Starfleet as a weapon to combat future Borg incursions and was first fitted onto the prototype USS Defiant. The device functions similarly to a standard Phaser, but without a continuous beam. The energy emissions are instead stored in a magnetic field, allowing them to coalesce and agitate to higher energy states. The field is then redirected, forcing the burst of Phaser energy toward the target. This process is repeated rapidly using multiple magnetic field generators, and the result is a stream of phased energy projectiles. Although the range of such a weapon is much less than the standard Phaser due to rapid dissipation, from close range the pulse Phaser can do more damage than most Phaser types. The weapon has since been adapted to function on most Federation ships."
According to the video game Star Trek: Elite Force II, the Sovereign-class USS Enterprise-E was also armed with a backup auxiliary twin pulse phaser cannon that was embedded into the primary hull. The cannon turret was capable of being manually operated by personnel in EVA suits.
The video game Star Trek: Armada II also describes the phaser cannon as a pulse phaser on board Defiant-class ships, the Defiant-class variant Incursion-class (β) ships, Iwo Jima-class (β) ships, Federation starbases, and pulse phaser turrets. The Klingon NuQ'DuJ-class (β) scoutships were also armed with this weapon. According to the Star Trek Online video game, by the 25th century phaser cannons have become standard armament on many Starfleet ships.