He has taken successive cases to the courts from inside prison, trying to get them to look at various grievances.
This includes unsuccessful appeals against his conviction and sentence.
The courts have variously described his suits as "vexatious", or ill-conceived and prone to failure.
Last month, Genge lost a High Court case against the Department of Corrections seeking to have his low-medium security classification declared unlawful. The possible costs against him in that matter are still being determined.
Genge has repeatedly been denied parole by the Parole Board. In various appeals to the court system, he has unsuccessfully argued that the Parole Act 2002 does not apply to him because it came in after he was sentenced.
In the latest case, Genge sought to reopen two disciplinary matters which went against him when he appeared before "visiting justices" in prison.
On one charge, he and another prisoner were found to be sparring in breach of prison rules in April 2017.
Genge argued that the sparring, in which his partner was holding up jandals as pads, was part of an exercise regime.
On the second charge, it was found that Genge refused to obey an officer's lawful order to return to his cell during a power outage in July 2019.
Objecting to the visiting justices' findings in the two matters, Genge appealed to the High Court for a judicial review and, when that did not go his way, took the matter to the Court of Appeal, which also found against him.
Genge then sought leave to apply to the Supreme Court, challenging factual findings in the earlier hearings, the validity of the prison "no-sparring" rule, the fairness of the charging processes for each of the breaches, and whether he had been properly informed about the power cut at the time he disobeyed the order.
The Supreme Court refused him leave to appeal, saying that most of the matters either did not raise questions of general or public importance, nor were sufficient to give rise to a risk of a miscarriage of justice.
The question of the no-sparring rule was considered insufficient in the interests of justice for the Supreme Court to consider it.
Genge was ordered to pay the costs jointly to the respondents in his latest case - the visiting justices, the Department of Corrections and the Attorney-General.
