Black Mask's Henchmen are a group of mobsters who obeyed the orders of Roman Sionis, aka Black Mask, in his criminal endeavors. They are also known as False Facers.
Before Arkham Origins Incident
Before the Christmas Eve Incident, Black Mask's men obeyed him due to his overwhelming strength and influence in Gotham City with only a few other gangs that stood in his way. It wasn't until the Joker took over the gang in disguise, that Black Mask's Henchmen had started to notice changes in their boss' personality such as a more light-hearted demeanor, a habit of joking around with his subordinates, and placing bombs under various buildings such as the GCPD Building, that a few henchmen started to question their leader.
Arkham Origins Incident
Black Mask's Henchmen were originally working with Black Mask, until the Joker impersonated Black Mask and usurped his gang. At the Gotham Merchant's Bank, a quarter of Black Mask's men were killed by Joker as he took Black Mask hostage. There were a few thugs that worked with Black Mask, when Batman tried to destroy the chemical containers, and when he went to the Church and Medical Center. The remaining loyal members of Black Mask's gang were sent to Blackgate Prison once Batman apprehended Sionis. The rest of Black Mask's thugs (then Joker's Henchmen) were seen working with the Joker. They ended up getting locked up in Blackgate along with him.
Cold, Cold Heart Incident
While Black Mask's men were nowhere to be found during the New Year's Eve Incident, it was assumed that they were apprehended and were put back in their cells at Blackgate.
Arkham Origins Blackgate Incident
Black Mask's Henchmen along with Joker and Penguin's men were first seen harassing Catwoman outside the Cell Blocks. Later, Black Mask's men were in the Industrial Building (as well as the Sewers if you were trying to get to the Joker). After the defeat of Black Mask, it's assumed that they were all apprehended.
Between Arkham Origins Blackgate and Arkham Asylum Incident
During the time between Batman: Arkham Origins and Batman: Arkham Asylum, Black Mask seemed to have lost a large amount of influence due to the number of super-villains who took over the criminal underworld. It could be assumed that some of Black Mask's gang were still working with Joker during the massive takeover of Arkham Asylum, or left for other gangs.
Before Arkham City Incident
Arkham City Incident
Black Mask's thugs were nowhere to be found in Arkham City. It could be presumed that they joined the Joker when he took over the Steel Mill, after their boss was captured, or split among the other gangs.
After Arkham City Incident
Black Mask reunited his gang and started his weapon deals again.
Arkham Knight Incident
Black Mask and his thugs didn't appear in that incident.