The youngster, who cannot be named, initially said the incident happened on Saturday 22 March 2014.
But in a later interview, he said he had "made up" that part and it had actually happened on a Tuesday.
Liam's mother Rachel Fee and partner Nyomi Fee deny murdering Liam and blaming his death on another child.
They are alleged to have killed Liam at a house near Glenrothes in Fife.
The mother, 31, and her partner, 28, are originally from Ryton, Tyne and Wear.
They also deny a catalogue of allegations that they wilfully neglected Liam and two other boys in their care by making them stand under cold showers, shut one in a dark room full of snakes and put a cage of live rats on another's head.
The jury at the High Court in Livingston has been shown various pre-recorded interviews with the child the couple are alleged to have wrongly blamed.
The trial heard last week that the boy told a police officer and social worker he had "strangled" Liam - but that the two-year-old was still sitting up and watching television afterwards.
The boy could be seen putting his hand to his face, over his mouth, before telling the interviewers he had used just one hand.
But in a later video played to the jury on day six of the trial, the boy said he "made up" the part about the incident happening on the Saturday.
"It was Tuesday," he told the interviewers.
He was later asked: "Do you understand what happened to Liam? How do you know that?"
The boy replied: "Cos I did it."
"You did it on the Tuesday?" the questioners continued.
"Yes," the boy replied, adding: "Put my hand over his mouth."
The jury also heard claims Rachel had been shouting at the boy on the day of Liam's death.
"Can you remember what she was shouting at you about on that Saturday night?" asked the interviewer.
"It was all my fault," the boy replied, adding: "Liam, it was all my fault."
The youngster also told how the accused took him to a "snake house" in the town where they lived where there was a big snake called Hunter.
He said: "Hunter is very... he's very big and he eats kids. So that's why most of the time he's in his cage locked up."
The court was again closed to the public as the recordings were played to the jurors.
The murder charge alleges the couple assaulted Liam at a house in Fife on various occasions between 15 March and 22 March 2014.
The pair deny all the charges against them.
The trial, before Lord Burns, continues.
A young boy who said he "strangled" toddler Liam Fee on the day he died changed his claim in a subsequent interview, a murder trial has heard.