Supreme Court Justice David Nahmias is looking to fend off a challenge from attorney Tammy Lynn Adkins in the runoff. He received roughly 48 percent of the vote in the Nov. 2 election, compared to 35 percent for Adkins.
Since neither candidate receive 50 percent plus one vote, a runoff was set.
Meanwhile, Antoinette Davis and Chris McFadden are vying for an open seat on the state Appeals Court. Voters must also pick Superior Court judges for the Atlanta, Macon and Stone Mountain circuits.
The races are nonpartisan. Polls closed at 7 p.m.