During the hearing, Judge Christopher Cooper of Federal District Court in Washington suggested the next court date for the man's case to be held on 4 May.
But this caused Barnett, 60, to erupt over the proceedings being extended for a longer period of time while he remained in jail.
Watch: Richard Barnett replaces attorney
“I’ve been here a long time ... another month ... It’s not fair,” Barnett was heard saying about the new court date, according toNBC4. “You’re letting everyone else out ... I need help,” he yelled.
Following the outburst, the judge called for a five-minute recess so Barnett would be able to speak to his lawyers. He is represented by the law firm of Metcalf & Metcalf, and the McBride law firm.
Judge Cooper then confirmed that the next hearing would be set for 4 May after court reconvened. But he told Mr Barnett that his lawyers could make a bail application on his behalf and then a separate hearing date could be scheduled.
Mr Barnett has been charged with aiding and abetting, disorderly conduct in a capitol building, parading or demonstrating in a capitol building, and theft of government property for his alleged actions on 6 January.
The man went viral on social media after photos circulated of him with his feet up on the House Speaker's desk as well as holding Ms Pelosi’s mail outside the US Capitol.
For the last few weeks, Mr Barnett has been in jail after he was arrested from his Arkansas home. He pleaded not guilty to all charges when first appearing in court and was being held without bond until his trial.
So far, about 300 people have been charged for their alleged roles in the Capitol riots that took place on 6 January following a pro-Donald Trump rally in Washington DC.
The FBI and Justice Department have utilised a variety of means including gathering social media posts, video footage, and pictures to help identify as many people as possible who were involved in the riots on that day.
Watch: 'Quick reaction force' recommended after Capitol security review