Abba, who was arrested last July, faces charges of "complicity in terrorism and failing to denounce acts of terror", according to the charge sheet read in the court in Yaoundé.
He denies the charges and his lawyers want the trial scrapped, arguing that his detention is "arbitrary and illegal".
They also say that he was initially denied access to his family and lawyers and kept in chains "like in Guantanamo".
Abba is accused of acting as an accomplice to two members of Boko Haram, which is based in Nigeria but active in northern Cameroon, where the government says it has killed 1,200 people since 2013.
Prosecutors also accused him of failing to warn the authorities of "activities by the Boko Haram sect".
Cameroon introduced capital punishment for involvement in terror attacks or complicity in terrorism in a controversial law passed in 2014.
"Glorification of terrorism" also carries heavy penalties.