This work performs an analysis of plasma-assisted non-premixed H2-air flames in Y-shaped micro combustors in the presence of field emission dielectric barrier discharge (FE-DBD) plasma actuators. The combustion, flow, and heat transfer characteristics are numerically investigated, and the effect of sinusoidal plasma discharges on combustion performance is examined at various equivalence ratios (φ). A coupled plasma and chemical kinetic model is implemented, using a zero-dimensional model based on the solution of the Boltzmann equation and the ZDPlasKin toolbox to compute net charges and radical generation rates. The estimated body forces, radical production rates, and power densities in the plasma regions are then coupled with hydrogen combustion in the microchannel. Plasma-assisted combustion reveals improvements in flame length and maximum gas temperature. The results demonstrate that FE-DBDs can enhance mixing and complete the combustion of unreacted fuel, preventing flame extinction. It is shown that even in cases of radical and thermal quenching, these plasma actuators are essential for stabilizing the flame.