Abstract: In this work, the effects of transverse boundary conditions, specifically the bias voltage on the transverse wall and the gap width, on the electron beam-generated plasmas (EBPs) confined in a narrow gap, are investigated using the particle-in-cell/Monte Carlo collision (PIC/MCC) simulations. Simulation results reveal that the application of bias voltage causes beam deflections, leading to the formation of band structures in the beam electron velocity space. Three branches of electrostatic waves, including electron beam mode, Langmuir wave, and electron acoustic mode, are identified. Increasing the bias voltage and reducing gap width intensify beam deflections, resulting in the suppression of waves. Both wave excitation and beam deflection significantly modify beam electron transport, leading to the plasma non-uniformity. These findings enhance the understanding of beam transport and plasma behavior in discharges confined in a narrow gap.