The 31-year-old was wanted by Dubai authorities for allegedly passing on fake money during a trip to the United Arab Emirates last year.
Billy has denied the accusations, saying he was cleared of the crime following an investigation.
But his passport has been seized and he's unable to leave the country while he faces court proceedings, the Daily Record reports.
Billy was arrested when the family arrived in Dubai for a holiday
Billy, from Edinburgh, was pulled aside by immigration officers when the family landed at Dubai's airport last month.
He said he was held in shackles for three days before being released on bail, and he remains in the country after his devastated family had to return to the UK without him.
Speaking from Dubai, Billy said: "We tried telling them about the mix-up last year but for some reason I was still in the computer as wanted for passing on fake money.
"I was held in shackles for three days in a cell away from my family."
His partner Monique spent the rest of the holiday trying to get help from the British Embassy, but she and the couple's children, nine-year-old Madison and seven-year-old Billy Jnr, were forced to fly back to Edinburgh alone.
Billy was forced to stay in Dubai while his family returned home
Billy is now facing up to a year in prison for a crime which he says he didn't commit and was cleared of last year.
The plasterer's first brush with the law came while the family enjoyed a sunshine break in Dubai last year.
The family had gone to change some money at an exchange in Al Hamra Mall. But one of the notes handed over by the couple set off the counterfeit money detector and they were told to wait for the police.
The whole family were then hauled off to the Ras Al Khaima CID headquarters, where Billy was interrogated for 12 hours while their hotel room was searched.
After no counterfeit money was found, the family were released and told they faced no charges.
Billy with Monique and children Billy Jnr and Madison
Monique, 42, said: "The relief was huge. I mean, we knew it was a mix-up.
"Either someone had given the note to Billy as change or maybe the detector machine was faulty.
"There was certainly no intent from us to steal £20, but until you're released, you can't help but be frightened."
Billy added: "It was distressing for the kids to see their dad arrested. They have never been in a police car or police station.
"Myself and Monique reassured them – we knew that the police would investigate and see that it was an honest mistake.
"I even double-checked with the police. I asked them if we were clear to carry on our holiday, and also to come back to the UAE again.
"They told me, 'Absolutely yes', and that they wouldn't have released me unless I was cleared."
Monique says the couple's children have been left devastated
But the family's world was turned upside down when they returning to Dubai on September 15.
Billy, whose savings have dwindled as he's forced to pay for hotels while remaining on bail, said: "If I were to be handed a prison sentence, it would cripple us financially.
"I just pray our family can be back together again soon."
Monique added: "We just need him home. The kids cry every day. Billy normally coaches his son's football team three evenings a week, and those times are especially hard.
"The kids can't even speak with him on the phone because they get so upset."
Radha Stirling, the CEO of British NGO Detained In Dubai, who is supporting the family said: "Clearly in this case, Mr Barclay received a counterfeit note that was already in circulation and is himself a victim.
"Charging him over a fake note he received and passed on unknowingly is not an effective way to deal with the problem of counterfeiting.
"It once again highlights the risks visitors to the UAE face from the country's legal system, which has not been developed as fast as the skyline has.
Billy had his passport seized after he was detained in Dubai
"Mr Barclay was shocked by the charge, and is already suffering unduly because of the proceedings.
"We hope that the charges will ultimately be dropped, but in the meantime Mr Barclay is in a very difficult situation.
"We are continuing to support him throughout the judicial process and hope for his speedy release."
Edinburgh South MP Ian Murray is working with the Barclay family to try to get Billy home.
He said: "I have been in contact with the Foreign Office and the Dubai authorities and am working closely with the family to try to get this situation resolved."
An FCO spokesperson said: "We are providing assistance to the family of a British man who was arrested in UAE in September."
Mirror Online has contacted Dubai Police for comment.