Restricting the injection of cations is crucial for implementing precise quantized conduction (QC) during the multi-level operation of conductive-bridge random-access memory (CBRAM). This study proposes a method that controls ion supply by confining the Cu ion source to 0D in a vertical structure. This confinement enables sophisticated filament control for multilevel operation. Cu nanodots are formed between the W electrodes, with W and Cu serving as the electron and ion sources for the conducting filament, respectively. When the Cu filament is confined to 0D, the controllability of the QC implementation is better than that in cases where the filament is restricted to 1D or bulk Cu. The highest number of quantized levels was observed for 0D Cu, which can be attributed to the synergistic effects of filament confinement and the decrease in the Cu electrochemical reaction rate. Furthermore, we analyzed the switching mechanism of the Cu nanodots by employing the activation energy extracted by the slope of the voltage-time dilemma. Our results demonstrate the effectiveness of confining the ion source to 0D for achieving precise filament control in CBRAM and enabling its applicability to vertical structures.