In the past decade resistance-based memory devices, or the resistive random access memory Devices (RRAM) have emerged as a potential candidate for multi-state memory storage and non-conventional computing applications. Reports on conduction quantization (QC) have added an interesting layer to the utility of these RRAM devices for ultra-dense memory and neuromorphic computing applications due to the occurrence of integral and half-integral conduction (resistive) states. Since the first reports of QC phenomena in RRAM devices, there have been detailed studies on the nature of the conducting filaments, switching mechanisms, and tunability of the QC states, but there exists a scarcity of studies exploring controllability of QC phenomena in scalable device geometries. In this work, we report compliance current controlled tunable QC phenomena in crossbar RRAM cells based on electrochemical metallization switching mechanism. The devices exhibited robust bipolar resistive switching, with well separated high and low resistance states.  The magnitude and number of the QC states were found to increase from ~2.5 to 3.5 and from 4 to 6, respectively as the IC increased from 50 to 200μA. The Cu/Ta2O5/Pt device structure was chosen to strategically govern the metallic nature of the conduction filament (CF) formation, which helped postulating factors contributing to the tunability of the states via compliance current. We report the lateral dimension variability as the main factor governing the magnitude and number of quantized steps observed in RRAM devices, where we also discuss a numerical method to approximate the diameter of the CFs. The increase in number and magnitude of QC steps with IC was explained considering the fact that thicker CF obtained at higher ICC, when undergoes a gradual rupture during reset process, results in larger number of QC steps compared to a thinner CF.