NEW YORK—An inmate on a New York City jail barge died Wednesday after a medical emergency, the city’s Department of Correction said. It is at least the 12th death of a city inmate this year and the second this week amid what some elected officials and advocates have deemed a “humanitarian crisis” in the city’s lockups. The Department of Correction said in a statement that the inmate at the Vernon C. Bain Center, a floating Bronx jail across the East River from the Rikers Island jail complex, appeared to be in medical distress and was taken to a hospital, where he was pronounced dead around 10:50 a.m. Correction Commissioner Vincent Schiraldi said he was “devastated to see that we have yet another death in custody, and determined to stop this heartbreaking trend.” “We are doing all we can to remedy the unprecedented crisis we are experiencing in our jails. My …