Scott Snowden, 39, was jailed for 33 years last summer for masterminding the murder of Thomas Sharkey, 55, his son Thomas Junior, 21, and daughter Bridget, eight, in a fire at their Scott Court home, on July 24, 2011.

Co-accused Robert Jennings, 51 – who set the fire by pouring petrol through the letter box on the instructions of Snowden – was jailed for 29 years. The pair were also convicted of trying to murder Mr Sharkey’s wife Angela, 48, who survived the blaze.

On Tuesday and Wednesday (today), August 19 and 20, lawyers for the men asked judges Lord Carloway, Lady Smith, and Lord Brodie, to quash their clients’ jail terms at the Court of Criminal Appeal in Edinburgh.

Snowden’s legal team believe that he should walk free from prison because they say trial judge Lord Matthews favoured the prosecution over the defence in his closing speech to the jury.

Jennings’s legal team believe the judge was also wrong to allow a piece of evidence to go to the jury which they say was inaccurate and prejudiced the case against their client.

On Tuesday, Snowden’s advocate Donald Findlay QC told the Appeal Court judges that Lord Matthews committed mistakes when he summed up evidence at the end of the case.

He said: “He was obliged to ensure that there was a fair and balanced summing up of evidence, representing both the position of the Crown and the defence.

“While the learned trial judge rehearsed the Crown case, he failed to remind the jury of a number of important aspects of the defence case and the criticisms offered by the defence of the prosecution case.” Passing sentence, trial judge Lord Matthews told the pair that it was the worst crime that he had ever been involved in with during his legal career.

He added: “These crimes were cowardly enough in themselves but it is also a common feature of them that you cynically recruited others to do your dirty work for you making sure that you had a cast iron alibi.

“It maybe thought that you were safe from prosecution, hoping that those who knew about your conduct would not alert the authorities.

“If that is what you thought, the fatal fire put an end to such aspirations.” Earlier, Mr Findlay said that when Lord Matthews summed up the case to the jury, he was too biased in favour of the prosecution. Mr Findlay argued that this meant his client’s conviction was unsafe and that it should be quashed. He added: “He ran the risk of making the pieces of evidence seem more important to the jury than they actually were.” On Wednesday, Jennings counsel Gary Allan QC told the Court of Criminal Appeal that there was not sufficient evidence to place Jennings as the perpetrator.

Mr Allan said: “Whilst there may be a basis for suspicion in this case it does not amount to more than suspicion.

“The jury would not be entitled to draw an inference from the pieces of evidence that he was the actor in the arson attack that gave rise to the three deceased in this case.

“In this case the limited evidence which there was did not include anything that could be regarded as decisive evidence the smoking gun kind of evidence.” Mr Allan argued that the trial judge, Lord Matthews, had erred in holding that taken as a whole there was sufficient to allow jurors to come to a view that Jennings “had been the actor who by means of petrol ignition set fire to the house with the catastrophic consequences.” He asked the judges to quash Jennings conviction and said that appeal grounds advanced on behalf of him raised matters which had resulted in a miscarriage of justice.

Advocate depute Alex Prentice QC told the court that the trial judge’s charge to the jury had to be looked at as a whole and submitted that there was a balance in it.

“What was done was not productive of a miscarriage of justice,” he said.

Mr Prentice also argued against the appeal ground advanced by Jennings that a no case to answer submission made on his behalf was wrongly rejected.

He said: “In my submission there was a case to answer. The trial judge was right to reject the submission that there was no case to answer.” The appeal judges reserved their judgement in the case and will give a decision at a later date.

Lord Carloway said: “This court has clearly got a lot to think about in relation to this case.”