Lawyers for the accused revealed that they filed the application at the apex court on Monday.
But the court said it did not have a copy and therefore gave them three days to put their house in order.
The case was adjourned to Monday, February 18, 2019.
Last month, the Attorney General (AG) filed a nolle prosequi to discontinue the trial of Gregory Afoko.
The application comes after the arrest of Asabke Alangdi.
According to Information Minister, Kojo Oppong Nkrumah, Asabke Alangdi, was arrested in Ivory Coast following a collaboration between Ghana's security agencies and Interpol.
"Ghana's security agencies working in collaboration with Interpol have arrested the second suspect in the murder of Mr. Adams Mahama, Former Chairman of the NPP in the Upper East Region. The fugitive AsabkeAlangdi was arrested in Ivory Coast after over a year of surveillance and search during which period he moved camps from Burkina Faso to Ivory Coast," he said at a press briefing.
The late Adams Mahama was gruesomely murdered in 2015 after his attackers poured acid on him in front of his home in Bolgatanga.
Investigations disclosed that his death was caused by the two persons, but the Police only managed to arrest the first suspect, Gregory Afoko.
The second suspect, Alangdi, however fled the jurisdiction in the days after the murder and has been on the run since.