His mother Nakala asked him to call police at about 4am when she felt threatened when a former partner turned up at their home in Indianola, Mississippi, Mr Moore said.
When two police officers arrived one kicked the front door before his mother opened it, he said.
She told them the intruder had left the home but three children were inside, he added.
Mr Moore said an officer shouted into the home and said anyone inside should come out with their hands up.
He said Aderrien walked into the living room with nothing in his hands, and was shot in the chest.
Ms Murry said: “His words were: ‘Why did he shoot me? What did I do?’ and he started crying. This cannot keep happening. This is not OK.”
The family is demanding the police officer is dismissed and charged with aggravated assault and have demanded bodycam of the incident is released.
Ms Murry said her son is “blessed” to be alive but he does not understand why a police officer shot him.
She described what had happened as “the worst moment in my life”, adding: “I feel like nobody cares - that’s my child, y’all.”
The officer involved has been placed on leave as the shooting is investigated.
The Mississippi Bureau of Investigation is conducting a probe into the incident.
The incident is the latest in a string of police shootings of unarmed black people in America.
The officer who shot the boy and has been suspended from duty is black, according to reports.
