An Everett man is facing charges of extortion and impersonating a police officer after he allegedly stopped a Dorchester couple and prevented them from providing medicine for a child having an ­asthma attack until they paid him cash “for his time and his gas,’’ Boston police said Monday.

John Perry Carrington, 44, was arrested on Callender Street around 12:30 a.m. Monday, ending an incident that ­began when the woman and her boyfriend, who had gone to buy medicine for an asthmatic child, cut off Carrington’s car while driving on Harvard Street near Deering Road.

After the couple made a U-turn and cut him off, ­Carrington allegedly responded by blocking their vehicle with his car, flashing a badge, and telling the couple he thought they were drunk.

Carrington also allegedly seized their cellphones and told the couple he would follow them home to Callender Street, where he expected to be paid $100 in cash “to avoid a citation,’’ police said.

After following them to ­Callender Street, Carrington ­allegedly forced the couple to stay in their car for 30 minutes even as they pleaded with him to let them enter their home to provide medication to a child suffering an asthma attack.

Carrington allegedly called Boston police during this time and pretended to be providing dispatchers with information on the couple, police said.

Carrington allegedly accepted a $20 cash payment and was still on the scene when officers, who ­received a call for an ­unknown situation, arrived. ­Police said he told them he knew the couple and was trying to help them, but could not tell ­officers their names.

He was arrested on charges of extortion, impersonating a police officer, armed robbery, larceny by false pretense, kidnapping, and unlicensed operation of a motor vehicle, police said.