Liam Adams is to seek to go before the European Court of Human Rights in a final bid to have convictions for raping his daughter overturned.
Lawyers for Adams, whose brother is Sinn Féin president Gerry Adams, confirmed plans to take their fight to clear his name to Strasbourg after all domestic attempts were exhausted on Friday.
Senior judges in Belfast refused to certify the case for consideration by the Supreme Court in London.
Rejecting defence submissions, Lord Chief Justice Sir Declan Morgan said: "None of these even get close to a point of law of general public importance."
Adams (60), is serving a 16-year-old jail sentence for a string of sexual assaults against his daughter Áine, who waived her right to anonymity.
The abuse was said to have been carried out between 1977 and 1983 when she was aged between four and nine.
Adams, formerly of Bernagh Drive in Belfast, consistently denied the allegations throughout a second trial at Belfast Crown Court in 2013. But a jury of nine men and three women found him guilty of 10 offences against his daughter: three charges of rape, four counts of indecent assault and a further three counts of gross indecency.
In May last year the Court of Appeal upheld his convictions after rejecting claims that those jurors were not properly directed on how to deal with widespread publicity in the case.
Defence counsel claimed the level of press, television, radio and online coverage on both sides of the Border even before he went on trial turned his case into a national issue. It was contended that guidance to the jury may have wrongly shifted the burden onto Adams to prove he was innocent.
A further criticism was levelled at the advice given on how to deal with the reliability of the alleged victim’s account.
But a panel of judges dismissed all grounds of challenge, ruling that the guilty verdict was in no way unsafe. Adams’ lawyers returned on Friday, seeking leave to appeal to the Supreme Court.
To be granted permission they had to establish a legal issue deemed worthy of further exploration.
Eilis McDermott QC centred her arguments on whether the jury was clearly and unambiguously directed on the burden and standard of proof.
However, the judge told her the points being raised were attempts to challenge the court’s conclusion, rather than raising any legal aspects of public importance. “We have no intention of certifying them,” he said.
The refusal closes off any route to the Supreme Court.
Outside court Liam Adams’ solicitor vowed to continue with the legal fight. Reg Rankin, of Breen Rankin Lenzi law firm, said: “Following the application before the Court of Appeal today we will be petitioning the European Court of Human Rights in Strasbourg to hear the issues relating to the appeal.”