Updated at 12:15 p.m.: Revised to include additional details about Rainey's criminal history.

Police have arrested a man they say admitted that he fatally shot his pregnant wife Sunday at a South Dallas home.

Lagarius Rainey (Dallas County Sheriff's Department)

Lagarius Rainey, 24, was booked into the Dallas County Jail around 2 a.m. Monday on a murder charge. He remains in jail, with bail set at $350,000.

Police were called about 7 p.m. Sunday to the 2600 block of Marburg Street, where they found 20-year-old Delashon Jefferson and her brother-in-law, 25-year-old Daveron Sanders, suffering from gunshot wounds.

Jefferson, who was 8 months pregnant, later died at a hospital. Doctors saved her baby.

A witness told police where Rainey had fled and what he was wearing, and police found him shortly afterward, according to an arrest-warrant affidavit. Officers handcuffed him, and Rainey told police he wanted to tell them why he shot Jefferson and Sanders, the affidavit says.

At police headquarters, Rainey told a detective that he was punching Jefferson during an argument because he thought she was cheating on him.

Jefferson started screaming, and her sister and brother-in-law came to the bedroom to see what was going on, according to the affidavit.

Rainey told police the two family members started punching him and, fearing for his life, he took out his gun and started shooting, the affidavit says.

Jefferson, who was shot in the back, ran out of the room and collapsed in the hallway. She was taken to a hospital, where doctors performed an emergency C-section. Jefferson died, but her baby survived.

Sanders, the brother-in-law, was hospitalized for a gunshot wound in his chest and was stable.

Rainey had "a history of family violence," police wrote in an arrest-warrant affidavit two years ago.

He was arrested in March 2016 on four counts of aggravated assault with a deadly weapon. Three of the charges stemmed from a March 4 incident in which police said Rainey woke up Jefferson, who was visiting him at the time, and told her he wanted to have sex. She said she didn't want to have sex, and he pushed her to the ground and punched and slapped her, according to an arrest-warrant affidavit.

Rainey's mother, whom he lived with and whose house they were in, tried to break up the fight but Rainey threw her into the refrigerator and punched her, according to the affidavit. When Rainey's sister's boyfriend tried to break up the fight, Rainey went to his bedroom, got a gun from under his bed and fired it, the affidavit says. A bullet grazed his mother's thumb, but no one else was injured.

When he was arrested, police learned Rainey also had a warrant out for his arrest for another aggravated assault charge.

Police said Rainey and Jefferson had been dating for about five years in February 2016, when they got into an argument over the phone, according to an arrest-warrant affidavit.

After the argument, Rainey went to Jefferson's apartment. When she opened the door, he grabbed the back of her neck and scratched her, pulling her out of the apartment. He then hit her in the head with a handgun before she was able to run away and call police, the affidavit says.

For each of the four assault charges, Rainey was sentenced to four years of deferred community supervision. The sentences were being served concurrently.

In 2015, Rainey was convicted of a misdemeanor count of unlawful carrying of a weapon. He was sentenced to 30 days in the Dallas County Jail.

CORRECTION, 2 p.m., Sept. 25, 2018: An earlier version of this story included incorrect ages for Jefferson and Rainey, due to incorrect information provided by police.