Quate's wife says that he killed their youngest daughter in 2013 and left her body in a bin in a garage of an abandoned home in Centreville. Police in IL found the body, but no charges have been filed in the girls death.
Authorities suspect the child was killed in nearby Belleville in 2013 and taken to the Centreville garage.
Police found that body early Tuesday morning.
Jason Quate made the comment Thursday during an interview with the St. Louis Post-Dispatch (http://bit.ly/2rQDrBt ).
A search warrant was served in Las Vegas, and early Tuesday morning, Quate was arrested on sex trafficking charges.
Officers found a child's remains Tuesday in the garage behind a vacant home in Centreville, Illinois, after a woman in Las Vegas contacted police.
"She stated that her husband was extremely abusive and had forced her to go out and solicit herself for prostitution and also was physically abusive to the children", said Lt. Raymond Spencer with Las Vegas Metropolitan Police.
He said investigators from the Illinois Division of Children and Family Services came to their house, and he and his wife panicked.
Detectives in Las Vegas said Quate was abusing his daughters at their apartment.
Quate told the Post-Dispatch that the girl choked to death when he spanked her, unaware that she still had Salisbury steak in her mouth.
In his interview with the newspaper, he repeatedly referred to what happened with his daughter as "horrible".
Quate's wife alerted authorities about the body on June 5th after she sought refuge at a women's shelter.
Las Vegas police said the tip about the child's body stemmed from an unrelated investigation there. Both children were taken into protective custody.
Las Vegas police said they received one call in February 2017 to check the welfare of occupants at the Quates' address.
The girls were found in an apartment where police said they were never allowed outside, even to attend school. Police are seeking sex trafficking and child abuse charges.
The child-abuse allegations stem from the condition in which Las Vegas investigators found his other two daughters living.
A judge is expected to appoint a lawyer to represent him at the court hearing.
Belleville police will be going to Las Vegas as part of the investigation into the child's death.
"Obviously I am the victim here", said Jason Quate during an interview from the Clark County Detention Center. Centreville is an impoverished just across the Mississippi River from St. Louis. The coroner in St. Clair County said an autopsy was planned.