Authorities say the children are 12 months old and 10 days old. Neither was hurt in the New Year's Day shooting, and police say they are not related to the deceased man, 23-year-old Cristian Pena.
Investigators say multiple shots were fired at the building around 8 p.m. Monday. Pena was hit at least once in the chest.
He was pronounced dead after being driven to a hospital by friends.
Police say the shooting might be gang-related.
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