Police say Cedgadrick Ardarius Harris, 24, surrendered on Monday.
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According to investigators, Harris kicked in the front door of 28-year-old Kimberly Robinson's apartment around 4:20 a.m. Friday in the 1800 block of Barker Cypress Road.
Robinson and her 4-year-old daughter were inside the bedroom where at least six shots were fired.
The little girl was hit with shrapnel at least twice, but she was reportedly conscious and breathing at a hospital.
Four other children were downstairs at the time of the shooting, including a 10-year-old who called relatives for help after it happened, Houston Police Lieutenant Christopher Bruce said.
None of the other children were hurt. They have been placed in the care of relatives.
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Police and neighbors both told ABC13 there has been a history of domestic violence at the apartment.
"I was just praying she was OK," said one neighbor. "You know, hopefully nothing bad happened to her or the kids, but I knew somebody got hurt."
The victim had reported at least one domestic violence incident to police about a month ago, according to Houston Police Sgt. Michael Casso.
"This is my second domestic violence related homicide in the last couple weeks," Sgt. Casso said. "Naturally, when you get people together in quarantine for long period of time, sometimes tempers flare. I don't know. He's been out of this apartment for possibly months, so I can't say."