In this study, two-dimensional simulation of the microplasma field-effect transistor (MOPFET) was performed using COMSOL Multiphysics along with BOLSIG+ software and LXCat database. At first, argon plasma generation in the electric discharge channel was investigated in the case of an RF-biased drain terminal. The Townsend criterion for self-sustaining discharge was modified by including ion-enhanced secondary ionisation concerning to the micrometer scale of the discharge gap. The simulation results showed that the level of the gate electrode voltage serves as a tuner for the MOPFET current, and it changes the gas breakdown voltage. The results of the 2D simulation showed that the polarity of the gate voltage is crucial for controlling the MOPFET current and the operation of switching circuitry. To increase current, a new gas mixture was proposed and simulated. The $I_{DS}$−$V_{DS}$ characteristic of the MOPFET was obtained with Ar/Hg (98:2). Static transconductance and $h_{FE}$ of the MOPFET were also evaluated. The results of this study can be used for designing and operating the MOPFET in an electronic circuit.