Trump has argued the order violates his First Amendment rights, while special counsel Jack Smith's office says the former president is trying to influence and intimidate witnesses.
The judge found that Trump "engaged in insurrection" by inciting the Jan. 6 riot, but said he could still appear on Colorado's primary ballot next year.
The New York Republican's original complaint accused Judge Arthur Engoron of exhibiting “clear judicial bias” against Trump and called on him to recuse himself.
New York Judge Arthur Engoron ruled that the Trump team's arguments that he and his law clerk are biased against the former president were "utterly without merit."
A lower court judge denied a liberal group's effort to bar the former president from the state ballot under the U.S. Constitution's insurrection clause.
Fulton County District Attorney Fani Willis' office argued the judge needed to take the step “to protect witnesses and to safeguard sensitive and confidential information.”