November 06, 2015 12:20 PM

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In a new interview with Barbara Walters on Investigation Discovery, John Ramsey says he desperately tried to shield his son Burke from the tabloid headlines that accused him of murdering his 6-year-old beauty queen sister, JonBen t Ramsey.

“We tried to shield him from that,” John says in the interview. “Friends would ask us, ‘What can we do to help?’ We said, ‘Next time you go in the supermarket, call the manager over when you see our child’s photo on the front cover, and ask him to remove it.’ A lot of them did that.”

The interviewed aired Monday night on the new Investigation Discovery show, “Barbara Walters Presents American Scandals.”

JonBen t was found dead in her parents’ Boulder, Colorado, basement the day after Christmas in 1996. She had duct tape over her mouth and showed signs of an apparent sexual assault. (Read PEOPLE’s original story on JonBen t’s murder.)

Police investigated JonBen t’s parents, John and Patsy, and her brother at length in connection with the 6-year-old’s murder. But they were never charged in the crime, and in 2008 – two years after Patsy’s death form ovarian cancer – former District Attorney Mary Lacy cleared the Ramseys and Burke of any wrongdoing, citing third-party DNA evidence that was found on JonBen t’s clothing.

But in 2013, Jim Kolar, a former lead investigator on the case, told PEOPLE that Lacy was “overreaching” when she exonerated the three Ramseys. “The absence of other family members’ DNA in JonBen t’s underwear doesn’t necessarily rule them out as being involved or in covering up the murder,” he said.

John and Patsy have maintained their innocence in multiple interviews through the years. Burke, now a 28-year-old computer software developer, has never spoken publicly about the murder.

In the new interview, John says he holds out hope that his daughter’s killer will one day be caught. “I think we will have two ways that will happen,” he tells Walters. “It will either be a DNA match or someone who knows something will become angry or bitter against this person and will tell.”

After the murder, the Ramseys never again set foot in their Boulder home and moved to Atlanta, and the family had financial problems.

“I was told by an experienced FBI person at that most victims of violent crime end up broke,” Ramsey tells Walters. He said that a victim of a tragedy should “give your checkbook to a friend.”

Earlier this year, former Police Chief Mark Beckner admitted in a Reddit “Ask Me Anything” session that the case was mishandled. “It was the Christmas holiday and we were short staffed, we faced a situation as I said earlier that no one in the country had ever seen before or since, and there was confusion at the scene as people were arriving before we had enough personnel on the scene,” he wrote.

“I wish we would have done a better job of securing and controlling the crime scene on day one,” he added.

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