The controversy arose from a petition Burkhart filed with the state Supreme Court arguing that Republican Howard Strauss, who defeated Burkhart in the general election last year, cannot hold office because he filed for the seat from a magisterial district that was already occupied by another commissioner.
Two weeks ago, the Supreme Court ruled in favor of Burkhart and turned the seat over to him.
The residents presenting the petition Thursday said they agree with the Supreme Court's ruling that only one commissioner can be elected from a magisterial district.
But they said that Wright, who lost to Strauss in the Republican primary last May, should now have a shot at Burkhart's seat in a special election.
Charlie Bain of Bunker Hill said he helped put together the petition because he believes many Democrats would have voted for Wright in the general election had he been on the ballot. Many voters believe their voting rights were denied as a result of the case, said Bain, a friend of Wright's.
"We believe West Virginia politics and, in particular, Berkeley County politics, suffered a major embarrassment by this repugnant situation," the petition states.
"It's such a terrible mixed-up mess," said Rose Freas, who signed the petition.
The petition was also addressed to Berkeley County Circuit Clerk Virginia Sine, Circuit Court Judge Ronald E. Wilson, who was a special judge in the case, and state Supreme Court Chief Justice Margaret Workman.
A Supreme Court spokeswoman said Sine, Wilson and Workman could not respond to the petition.
The Supreme Court ruled in favor of Burkhart May 13. Strauss reacted to the ruling by calling it the "height of crooked politics in West Virginia."
Strauss filed a petition for a rehearing of the case before the Supreme Court, but the court turned it down, officials said.
The commissioners had planned to swear in Burkhart Thursday during their regular meeting. But that had to be postponed until Wilson signs an order confirming the Supreme Court's decision, officials said.