A man has admitted shooting dead his three-month-old son in front of a US state trooper.

Adam Theall, 21, of Rome, New York, wept and had to sit down several times yesterday as he admitted killing his baby son Eithen in June.

Theall told a judge he had been partying with a friend the night before and was high on drugs when he grabbed a loaded shotgun from his mother's home and confronted police who were responding to a domestic disturbance report.

Theall was shot more than a dozen times by troopers when he refused to put down the weapon after shooting the child.

He pleaded guilty to second-degree murder and faces 25 years to life in prison when he is sentenced on November 18.