<p>The present study describes the formation of complex structures with the evolution of sheath-plasma instability in a novel glow discharge system regulated by specific combinations of plasma boundaries during different Negative Differential Resistance (NDR) regimes. The boundary conditions alter dramatically when biased grids are introduced in the presence of a low magnetic field, leading to both significant trapping of charged particles and constrained axial flow of charged particles inside the system. This results in the formation of intricate structures near the electrodes and the existence of sheath-plasma interactions within the system. The instability is thoroughly investigated using a variety of nonlinear techniques in order to comprehend the transition states and signal resilience in this discharge plasma throughout different NDR regimes. The non-stationarity in the time series domain is further enhanced by the transition energy modes identified using the empirical mode decomposition technique, which causes both low-frequency and high-frequency oscillations to interact with harmonic production during various discharge regimes. These low-frequency mode decomposition techniques suggest that sheath modulation resulting from insufficient electron supply across the biased grid is responsible for complex structure formation and associated sheath-plasma instability during the NDR regimes.</p>