under pain of
With the threat of undergoing something extremely bad or unpleasant as a punishment. (Often used in the phrase "under pain of death.") Under pain of having our pay docked, we were told we had to come in every Saturday until further notice to take care of the backlog in work. The prisoners were forced to march under pain of death from the POW camp across the burning desert.
on/under pain of something
(formal) with the threat of having something done to you as a punishment if you do not obey a command: They were forbidden on pain of death to talk to any of the other prisoners.We were told to pay within three days, on pain of a €1 000 fine if we didn’t.