Sources tell Eyewitness News that authorities were called to the home on Topping Drive in Riverhead just before 3 p.m.
Authorities then fatally shot the son, who had a weapon in his hand.
The mother, who is confined to a wheelchair, was taken to an area hospital. Her condition is unknown.
Neighbors say she was quiet and suffered years of domestic abuse. Several say she had triplet boys and at least two of them suffered from a mental illness.
Three Southampton Town Police officers were treated and released from the hospital.
Detectives from the New York State Attorney General's Office also responded.
The investigation is ongoing.