Judge Johnny Hardwick denied Republican Roy Moore's request for a restraining order to stop Alabama's canvassing board from certifying Mr Jones' victory. "I will be an independent voice and work to find common ground with my colleagues on both sides of the aisle", he added.
Mr Moore's attorney wrote in the complaint that he believed there were irregularities during the election and said there should be a fraud investigation and eventually a new election.
In his own statement after the results were certified, Moore repeated his charge that the election was "fraudulent".
The election result was a blow to President Trump, who gave Mr Moore his full-throated support, even as other Republicans distanced themselves following the misconduct allegations.
Moore, the first Republican to lose a United States Senate race in Alabama in 25 years, moved late Wednesday to block state officials from certifying the victory of his Democratic rival on Thursday afternoon because of "systematic voter fraud". But the certification went on as planned on Thursday, with Merrill, Alabama Gov. Kay Ivey and state Attorney General Steve Marshall - all Republicans - signing off on the proceedings.
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Alabama's canvassing board officially certified Senator-elect Doug Jones (D-AL) on Thursday.
He unexpectedly lost to Jones by about 20,000 votes in the special election to fill the Senate seat vacated by Jeff Sessions, who is now USA attorney general.
Doug Jones' campaign subsequently filed a motion to dismiss the complaint.
Jones and Moore were competing to fill the U.S. Senate seat that previously belonged to Attorney General Jeff Sessions. Shortly before the 1 p.m.
Mr. Merrill did not immediately respond to a text message.
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Moore, a far-right Republican dogged by accusations of sexual misconduct with teens in the race to fill the Senate seat of Attorney General Jeff Sessions, lost the December 12 election to Jones but refused to concede.
Odd lost the Republican primary to former Alabama Supreme Court Justice Roy Moore.
But Moore wouldn't concede. The complaint cites conspiracy theorist Richard Charnin as an election expert who said that the chances of the unofficial election results being accurate were "less than one in 15 billion".
Mr Moore denied the claims and said he has taken and passed a polygraph test to prove they are false. The complaint also noted the higher-than-expected turnout in the race, particularly in Jefferson County.
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