Comanchero gangster Axel Sidaros, 27, is serving a seven-year jail sentence following multiple trials and appeals in the ACT courts.

He has already shed two convictions, including one for attempted murder, since a June 2018 incident at the Calwell home of deposed Canberra Comanchero commander Peter Zdravkovic.

Despite Sidaros claiming he was not one of the four hooded men responsible for burning Zdravkovic's cars and shooting him in the left hand, his convictions for five offences, including arson and intentionally inflicting grievous bodily harm, have so far stood.

Having now exhausted all options in the territory's legal system, Sidaros, the son of McDonald's mogul Hani Sidaros, is seeking special leave to appeal against his remaining convictions in the High Court.

In his application, his lawyers argue Justice David Mossop, who conducted Sidaros' second trial, erred in concluding cartridges found at the scene of the incident came from the bikie's shotgun.

They claim this finding was not permitted by the evidence firearms expert Clive Roberts gave in the ACT Supreme Court retrial.

In any event, Sidaros' lawyers say, such a finding was prohibited by a pre-trial ruling that had imposed limits on the extent to which Mr Roberts' opinion could be used.

Sidaros' legal team further proposes to argue that Justice Mossop "intervened" in the judge-alone retrial and asked questions of Mr Roberts in a manner "contrary to the approach taken by the parties", who were being careful to comply with the earlier ruling.

The lawyers will ultimately ask the High Court to quash Sidaros' five remaining convictions and acquit him, saying the ACT Court of Appeal erred last year when it declined to do this.

The application for special leave to appeal is signed by Bret Walker SC, who is widely regarded as Australia's top silk, junior barrister Phillip English, and solicitor Michael Kukulies-Smith.

They will be up against three opponents, led by ACT deputy director of public prosecutions Anthony Williamson, who argue the application should be refused.

In their response, prosecutors say the application is "fatally" premised upon a flawed understanding of the pre-trial ruling and upon an "intervention" complaint never raised with Justice Mossop or in the Court of Appeal last year.

Sidaros' proposed High Court appeal is "devoid of merit", the prosecutors go on to argue, describing Justice Mossop's intervention in the retrial as "entirely unexceptional".

They also say Justice Mossop never made a finding based on Mr Roberts' evidence that the cartridges were fired from Sidaros' gun, citing comments to that effect from ACT Court of Appeal judges Justice John Burns and Acting Justice Verity McWilliam.

However, a dissenting judge of that court, Justice Michael Elkaim, is quoted by Sidaros' lawyers as having found Justice Mossop "intended to, and in fact did, go beyond the limits" placed on Mr Roberts' evidence.

The High Court is yet to indicate when, if at all, it will hear oral arguments about the application.

Sidaros will be eligible for release on parole this July, after three years and 11 months behind bars, even if his latest legal bid fails.

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