It happened on Saturday inside a home on the 6700 block of Jackson Street.
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Karell Young, 31, was charged with attempted murder, multiple counts of endangering the welfare of children and other related offenses.
While all four children were in another room, authorities say Young fired his gun following an argument involving his current and former partner.
The 29-year-old woman, who is the mother of Young's three children, sustained injuries to her face.
Young's current partner, who is the mother of his fourth child, was not injured.
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Authorities say an 8-year-old child called 911 to get help.
Young was arraigned Sunday morning and is being held on $3 million bail.
Resources for people attempting to exit unsafe relationships and people who are experiencing intimate partner abuse and violence are available by calling the National Domestic Abuse Hotline at 1-888-799-SAFE (7233) and Women Against Abuse at 1-866-723-3014.