The noun mugshot, which originated in U.S. slang, designates a photograph of a person’s face, especially in police or other official records.

This noun occurs, for example, in Belligerence and hostility: Trump’s mugshot defines modern US politics, by Chris McGreal, published in The Guardian (London and Manchester, England) of Friday 25^th August 2023:

Mugshots define eras.
Bugsy Siegel peering malevolently from beneath his fedora in a 1928 booking photo summed up the perverse romance of gangsters in the prohibition age.
Nearly half a century later, mugshots of David Bowie, elegantly dressed but dead-eyed after his arrest for drug possession, and a dishevelled Janis Joplin, detained for “vulgar and indecent language”, spoke to the shock waves created by 1960s counterculture.
Now comes what Donald Trump Jr described as “the most iconic photo in the history of US politics” before the booking picture of his father glaring into the camera was even taken. But whether deeply divided Americans view the first ever mugshot of a former president as that of a gangster or a rock star is very much in the politics of the beholder.

The noun mugshot is from:
– mug, designating a person’s face;
– shot, designating a single photographic exposure.

The earliest occurrences of the noun mugshot that I have found are as follows, in chronological order:

1-: From The Waco News-Tribune (Waco, Texas, USA) of Thursday 3^rd October 1935:

City Now Has Its Own Plant for ‘Mug’ Shots
Will Save $200 to $250 a Year by Developing Police Films

The Waco police department now has its own film developing plant, for finishing pictures of prisoners who are “mugged” by Lieut. Sam Fuller of the police identification bureau. Fuller expects to save the city between $200 and $250 a year by developing his own films instead of sending them outside.
A dark room and film finishing equipment has been installed in the city hall basement for the work. Now Fuller snaps the picture of the person being “mugged,” takes the film to the basement and in a short time has a print at a fraction of the cost the city has been paying. He estimates that the city has been paying about $25 a month for this work and he will be able to operate for a year on two or three months’ budget.

2-: From the review of the 1935 U.S. drama film We’re Only Human—review by Henry Sutherland, United Press Hollywood Correspondent, published in the San Francisco Chronicle (San Francisco, California, USA) of Thursday 12^th December 1935:

Roger Pryor plays the shutter-snapper convincingly opposite Joan Perry, who insists on being assured of Roger’s high aims in life before saying yes.
Yearning to become an arty photographer, Roger gives up working for the gazettes and sets up a fancy shop. He’s reduced at length to snapping “mug shots” of passers-by at two-bits a copy, the payoff coming when his abandoned news nose quivers accurately and one of his pictures traps a dangerous criminal.

3-: From the Waterloo Daily Courier (Waterloo, Iowa, USA) of Tuesday 7^th January 1936:

THIRD DEGREE NO MORE BIG FACTOR IN TRACING CRIME
Scientific Methods Take Place of Force and Brutality in Police Work.

Davenport, Ia.—(U.P.)—Such police methods as the “rubber hose and water” treatment, the third degree, and walking the chalk line have no place in the modern police department, a survey of the Davenport headquarters revealed.
Instead, officers of the law have supplanted these antiquated ideas for scientific methods, such as fingerprints, radio transmission to police cars, lie detectors and similar instruments.
[…]
An important part of every police station is the rogue’s gallery, in which photographs or “mug shots” of criminals are kept for policemen to view.
A careful classification of these photos makes possible a fresh picture in the minds of patrolmen and detectives to aid in recognizing fugitives.

4-: From The Daily Oklahoman (Oklahoma City, Oklahoma, USA) of Tuesday 28^th January 1936:

Lockwood Raps ‘Mug’ Shots For Driver’s License

The problem of identifying holders of the proposed new city drivers’ licenses will be left to the city council for decision Tuesday when the ordinance providing for licenses comes up for final passage.
This was decided after C. T. Lockwood, sponsor of the ordinance, objected to a proposal made by Orval Mosier, city manager, that pictures of drivers be placed on licenses. Lockwood objected to the expense and trouble involved in using pictures.
“If the licenses are to be practical at all, they must carry some definite means of identification,” said Mosier.