Recent development on distributed systems has shown that a variety of fairness constraints (some of which are only recently defined) play vital roles in designing self-stabilizing population protocols. Current practice of system analysis is, however, deficient under fairness. In this work, we present PAT, a toolkit for flexible and efficient system analysis under fairness. A unified algorithm is proposed to model check systems with a variety of fairness effectively in two different settings. Empirical evaluation shows that PAT complements existing model checkers in terms of fairness. We report that previously unknown bugs have been revealed using PAT against systems functioning under strong global fairness.