A 30-year-old Washington man, whose three children were killed when he threw a lighted can of gasoline into the apartment where they slept with their mother, was sentenced yesterday to serve a minimum of 50 years in prison.

D.C. Superior Court Chief Judge H. Carl Moultrie I, without comment, sentenced Darnell W. Jackson to three consecutive 13-to-45-year terms for second degree murder, plus a minimum two years for arson and nine to 30 years for assault with intent to kill. Jackson pleaded guilty to these charges four months ago.

Federal prosecutors, calling Jackson "an incorrigible criminal," had asked for the maximum sentence, which was 175 years.

Appearing before Moultrie yesterday, Jackson said that government psychiatrists, prosecutors and his own defense attorneys had conspired against him in the case. "I didn't intend to kill nobody," he said. "When I get mad, my hands just take off."

Jackson, who according to court papers has a history of drinking problems, has undergone court-ordered psychiatric examinations and has been ruled mentally competent. In August, he pleaded guilty to charges that on March 8, 1981, he threw an antifreeze can filled with gasoline into a first-floor rooming house apartment where his common-law wife, Rita Fox, was asleep with their three children.

The explosion spread a blanket of flames over the children: Darnell, 2, Anita 1, and Sheila, two months. According to court papers, Fox was struck in the head by the can when it crashed through the window but escaped from the tiny room at 214A Morgan St. NW before the gasoline exploded.

She, neighbors and firemen attempted to enter the apartment to rescue the children, who were heard screaming, but were driven back by intense flames.

According to an account filed by the prosecution, Jackson on other occasions had beaten and stabbed Fox during their five-year relationship, and only hours before the fire had been ordered by police to stay away from the apartment.

A few months before the incident, a Superior Court judge had ordered Jackson not to approach the family unless he was accompanied by a social worker. According to a government presentencing memorandum, Jackson had told a social worker he would kill Fox and the children if they were taken away from him.

He had come to the rooming house the evening of the fire demanding to see them, but Fox, who was 23 at the time, had refused and summoned police, who ordered Jackson to leave.

According to the government account, Jackson filled an antifreeze can with gasoline at a nearby service station, then went to a friend and asked for a match, saying "he was going to burn that bitch up."

Law enforcement authorities said Fox, who is afflicted with partial paralysis and a speech impediment as a result of polio suffered as a child, is unemployed today.