The characteristics of the discharge modes in the microplasma generated in a plasma display with a coplanar gap and an auxiliary electrode were investigated in accordance with various plate gaps and coplanar gaps. The measurement results of the discharge current peak time, discharge current, and luminous efficacy showed that modes 2 and 3 appeared in the microplasma in the cases of various plate gaps and coplanar gaps and that the luminous efficacy increased in mode 2 and decreased in mode 3. In addition, a stabilized microplasma in a plasma display with an auxiliary electrode was obtained when the plate gap was longer than the coplanar gap, and the maximum luminous efficacy was obtained when the plate gap was similar to the coplanar gap. According to the measurement results, the discharge modes and the parametric studies are attractive to obtain and design for high luminous efficacy in a plasma display with a coplanar gap and an auxiliary electrode.