Usage patterns
公正な〈事〉a fair ~ (judgment, trial, decision, etc.)
The judge handed down a fair verdict.
公正を期すto strive to ensure fairness/impartiality
Observers were stationed to ensure the fairness of the election.
公正に〈動詞〉to do something fairly or impartially
The judges tried to evaluate fairly.
〈事〉の公正さthe fairness of something
The fairness of the deal is being questioned.