Jones, 48, a right-wing shock jock, claimed for years that the Newtown school massacre was staged by “crisis actors” as part of a government plot to increase arms control laws in America.
A jury this month ordered Jones to pay $965 million (£854 million) in damages to countless families who have suffered rape, death threats and extreme emotional distress as a result of his lies.
Jones filed the requests Friday, alleging that Judge Barbara Bellis’s pre-trial rulings resulted in an unfair trial and “a substantial miscarriage of justice.”
His attorneys, Norm Pattis and Kevin Smith, wrote in the motion, “Furthermore, the amount of damages exceeds any rational relationship to the evidence presented at trial.”
“Yes, the families in this case have suffered terribly from the murder of their children,” Pattis wrote.
The attorneys further claimed that a lack of evidence linked Jones directly to people harassing and threatening the Sandy Hook families. Pattis said the trial resembled a “commemoration, not a trial”.
Christopher Mattei, an attorney for the 15 plaintiffs in Jones’ lawsuit, declined to comment but said he and other attorneys from the Sandy Hook families will file a brief objection to Jones’ request.
Twenty students and six staff were killed in the attack on Sandy Hook Elementary School in December 2012.
In recent years, Jones admitted that the shooting did indeed take place, then condemned the lawsuits and trials at his Texas-based Info Wars dishonest and a violation of his right to free speech.
An FBI agent responding to the shooting and relatives of eight children and adults killed in the massacre sued Jones for defamation and inflicting emotional distress for spreading the false story.
During the trial, relatives of the victims said in emotional testimony that they had been threatened and harassed for years by people who believed the lies told on Jones’s show.
Strangers came to their homes to take them in and confront them in public. People threw insulting comments on social media. Relatives said they had been threatened with death and rape.
The verdicts came after another Texas jury in August ordered Jones and his company to pay nearly $50 million in damages to the parents of another killed Sandy Hook child.
A third trial over the hoax claims, involving two more Sandy Hook parents, is expected to be held in Texas by the end of the year.