Rhys Eastwood, Mohammed Mukhtar and Andre Sang forced the man to call relatives and friends to beg for cash, threatened to shoot him in the head and only released him after his cousin handed over £1,500.
Officers later found a video on a mobile phone of the perpetrators mocking the victim.
The three, held on remand, were sentenced at Leeds Crown Court on Wednesday afternoon, August 3.
Judge Mushtaq Khokhar said of the victim: “He was held for almost five hours, it was a prolonged incident. He did not think he would get out alive.
"It was planned in advance and decided you were going to extort him one way or another.”
Prosecutor Alex Menary said Mukhtar was friends with the victim and invited him on the afternoon March 13 last year to smoke cannabis in his car, in which Sang and Eastwood were passengers.
Picking him up in a BMW, the victim was suspicious when the men began quizzing him about his access to bank cards.
In Chapeltown, he tried to run but was dragged back into the car by Sang who then pointed the gun to his head.
Eastwood also pulled out a large hunting knife and pushed it towards the victim’s stomach.
Driving the man to his own flat on Otley, the kidnappers wore masks and searched the property before taking his X-Box and TV, while mocking him that he had nothing worth stealing.
They then put him back in the car and drove around demanding he start ringing his relatives, including his mother and father, who could hear the fear in his voice and threats being made.
An ex girlfriend gave up £300 and his cousin offered £1,500, which was passed to the kidnappers at 8pm in exchange for the victim.
After being arrested, Eastwood made no comment while Mukhtar gave a full statement, but denied the victim’s account.
Sang was arrested 10 days later.
The firearm, a BB gun which looked real, was later found, while Eastwood’s fingerprints were also found at the victim’s flat.
ANPR cameras had picked up the BWW and corresponded with the victim’s version of events.
Mukhtar, age 22, of Ederoyd Mount, Stanningley, was found guilty after a trial of kidnap, possession of a firearm with an intent to cause fear of violence, and blackmail.
Eastwood, age 23, of Bellbrook Grove, Harehills, was also found guilty of the same offences and admitted an unrelated street robbery from January 2020.
Sang, age 20, of Cowper Street, Chapeltown, admitted the kidnapping, firearm and blackmail charges.
Mitigating for Sang, Kara Frith told the court: “He accepts his choices and takes full responsibility. He gives a very candid account, and admits he brought the gun with him.
"He has tried to be as honest as he can.”
Barrister Becky Janes said Eastwood was bright with 10 GCSES, and had hoped to study history at university, but was thought to suffer from a borderline personality disorder.
For Mukhtar, Julian Jones said his client was “clearly a man of some intelligence”.
Eastwood was handed 11-and-a-half years’ jail, Mukhtar given eight-and-a-half years and Sang five years and 10 months.