Scott Peterson asserts his innocence in prison interview in new document

Speaking over a grainy video call feed in the noisy day room of Mule Creek State Prison in Ione, California, Scott Peterson seems more like a relaxed surfer than a man convicted of the heinous murder of his wife, Laci, and their unborn son, Conner.

His hair, sometimes tied in a ponytail, is long and tousled, his demeanor calm and friendly. At one point he becomes emotional as he recalls saying goodbye to Laci, then eight months pregnant, as he left the couple's home in Modesto, California, on the morning of Christmas Eve 2002 – the last time, he says, he saw his wife alive.

“Last Saturday someone mentioned [of the anniversary]and I was stunned,” says Scott, 51, wiping his eyes. “A guy I never expected humanity from, a guy I worked with in the kitchen that day, brought up the subject.”

But as he speaks on camera for the first time since his arrest 21 years ago, Scott is looking for much more than just the sympathy of a fellow inmate.

In Face to face with Scott Petersona new three-part docuseries premiering Aug. 20 on Peacock, the former fertilizer salesman — now serving a life sentence without the possibility of parole — again denies any involvement in the disappearance and death of Laci and the child she was carrying. He is appealing to the public to hear his side of the story, which he describes as a “so-called investigation” conducted by police and prosecutors who he claims ignored key clues and relied solely on circumstantial evidence in their effort to convict him of double murder during his 2004 trial.

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Scott says: “I regret not having testified [at my trial]but if I have the chance to show people the truth and if they are willing to accept it, that would be the greatest thing I can achieve right now – because I did not kill my family.”

The Peacock documentary – one of two about Laci's murder to be released this month – also documents the appeal the Los Angeles Innocence Project launched last January to overturn Scott's conviction by proving his innocence.

And one of Scott's most loyal supporters in the documentary, his sister-in-law Janey Peterson, who, among other things, became a lawyer to fight for his freedom, tells PEOPLE the project is also an opportunity to present the public with an alternative theory about what might have happened to Laci.

“My belief in Scott's innocence is not based solely on what he claims,” ​​she says. “My belief is based on the evidence.”

It was just after 6 p.m. on December 24, 2002, when Scott called Modesto police to report his wife missing. By the time investigators arrived at the couple's home, nearly three dozen friends, family members and neighbors had gathered in the quiet suburban neighborhood searching for Laci.

Scott told police he last saw his wife at 9:30 a.m. that morning when he drove 90 miles to San Francisco Bay to go fishing. In the documentary, he recounts “the things I enjoyed” about that final day.

“I saw Laci's smile as she did her hair on the morning of the 24th, and how we shared a bowl of cereal because we were too lazy to make two bowls,” he says. “Those little things are still with me.”

Investigators interviewed in the document say they quickly zeroed in on Scott, in part because husbands, boyfriends and other domestic partners are statistically more likely to commit violence against women. But Scott also aroused authorities' suspicions because of his casual demeanor and because he referred to Laci in the past tense during his first interview with police.

Scott claims that Allen Brocchini, a Modesto Police Detective and lead investigator on the case, “had already made up his mind before he arrived.”

Detectives doubted the authenticity of a loving voicemail Scott had left for Laci earlier that day on the drive back to Modesto – and suspected he had left the message after Laci's murder to provide himself with an alibi.

Looking back on it now, Scott is outraged. “They think it's too sweet a message for a married couple,” he says. “If they think like that, their marriage will really be a sad one. Frankly, I feel sorry for them.”

On December 30, 2002, the investigation took a dramatic turn when investigators learned that Scott was having an extramarital affair with a massage therapist named Amber Frey of Fresno, California.

Scott now admits he made a terrible mistake. “It's awful,” he says. “I was a total asshole for having sex outside of our marriage.” But he insists he didn't tell police he was in a relationship with another woman because he wanted to keep the focus on finding Laci.

“During the so-called investigation, I really did everything I could to bring my family home,” he says. “That included keeping my affair with Frey a secret from people. I didn't tell anyone because I wanted the search to continue.”

On April 18, days after the decomposed bodies of Laci and Conner washed ashore, about two miles from where Scott was allegedly fishing, he was arrested in La Jolla, California.

He had dyed his hair blonde and was carrying $15,000 in cash, a bag full of Viagra pills, camping equipment and four cell phones in his car. Police said he was just 30 miles from the Mexican border and preparing to flee.

“I don't understand this at all,” says Scott, who explains that he was visiting his family in San Diego and dyed his hair to avoid being recognized and verbally attacked by the public. “I just want to make it clear: I never ran from the police.”

During his five-month murder trial, which ended in November 2004, prosecutors described Scott as a man who regretted becoming a father and who committed murder to get out of his marriage without having to pay spousal and child support.

“This is so offensive and so disgusting,” he says of the prosecutors' allegations. “I definitely regret cheating on Laci, absolutely. It was about a childish lack of self-esteem, about my selfish traveling somewhere, about the loneliness that night because I wasn't home. Someone makes you feel good because they want to have sex with you.”

As the LA Innocence Project’s appeal against Scott’s conviction is heard in the California courts today, Face to face Director Shareen Anderson, who interviewed Scott via video from prison for a year, says the inmate is “optimistic and confident” that ongoing efforts to free him will be successful.

On May 29, a judge granted his lawyers' request to conduct DNA testing on the tape found on Laci's body, but denied testing on 16 other pieces of evidence. Scott, however, is patient.

“People want the answer they believed in to remain the answer,” he says with a cool smile. “We're all slow to admit when we're wrong.”

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