Two stars of Discovery Channel's reality-documentary series "Alaskan Bush People" pleaded guilty on Wednesday to submitting fabricated residency documentation with the purpose of collecting dividends from Alaska's Permanent Fund, according to Fox News. However, their plea deal was rejected by a judge.

Billy Brown, 62, admitted in a signed statement that he falsely claimed the Permanent Fund dividends from 2009 to 2012 by submitting paperwork that stated he was a resident of Alaska when in fact he was living out of the state.

"By submitting falsified PFD applications for myself and my children, I stole $7,956 from the people of Alaska," Billy Brown wrote in the plea deal statement, according to the Alaska Dispatch News. Billy Brown's 31-year-old son Joshua Brown also falsely claimed dividends to the tune of $1,174.

The two agreed to reimburse the state of Alaska the dividends they fraudulently collected and also agreed to two years of probation and 40 hours of community service.

The deal also asked for the dismissal of charges against four other Brown family members. The Brown family collected a total of $20,938 in dividends by Permanent Fund applications, according to Juneau Superior Court judge Philip Pallenberg, KTUU reported.

However, the plea deal was rejected by Pallenberg on Thursday. "I don't think the Browns should be treated more harshly because they have a TV show. ... But they certainly shouldn't be treated more leniently because of that either," Pallenberg said, adding that a 30-day jail sentence would be an appropriate punishment for the crime. The next hearing in the case has been scheduled for Dec. 3.