Mr Moore has not conceded the race to Mr Jones and has sent several fundraising emails to supporters asking for donations to investigate claims of voter fraud.
"Also provided in the complaint is an affidavit from Judge Roy Moore stating that he successfully completed a polygraph test confirming the representations of misconduct made against him during the campaign are completely false", Moore's campaign said in a press release. Janet Porter, a Moore spokeswoman, said earlier on CNN that the chances of voter fraud not having an effect on the election were astronomically low.
Alabama Secretary of State John Merrill is slated to certify the special election results Thursday.
Prior to the certification the Secretary of State's office noted that Jones' final margin of victory was 21,924 votes, AL.com reported.
Jones defeated Moore on December 12 by 21,924 votes in a stunning victory in a traditionally red state, becoming the first Alabama Democrat elected to the Senate victory in a quarter-century.
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Mr Moore has been accused of multiple sexual abuses involving children.
Montgomery Circuit Judge Johnny Hardwick on Thursday denied a last-ditch legal bid by Mr Moore for a restraining order to stop Alabama's canvassing board from certifying Mr Jones' victory.
Doug Jones' campaign subsequently filed a motion to dismiss the complaint.
Jones is scheduled to be sworn in as the junior senator from Alabama next week.
"I have stood for the truth about God and the Constitution for the people of Alabama", the conservative Christian said.
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Moore's attorney wrote in the wide-ranging complaint that he believed there were irregularities during the election, including that voters may have been brought in from other states. Alabama "will suffer irreparable harm" otherwise, the complaint argues, going on to urge state leaders to call a new special election.
"This is not a Republican or Democrat issue as election integrity should matter to everyone", Moore said in a statement Wednesday.
He will fill the Senate seat vacated by Jeff Sessions when Sessions became US attorney general in the Donald Trump administration early this year.
Merrill said he has so far not found any evidence of voter fraud, but he has said that his office will investigate any complaint Moore submits.
"It's a very weak complaint, it does not rely on any election experts I've ever heard of and it makes claims that on their face do not appear to be plausible, or appear to be irrelevant", said Rick Hasen, an election law professor at the University of California, Irvine.
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