Resistive switching and conductance quantization are systematically studied in a Ag/poly(3-hexylthiophene):[6,6]-phenyl-C61-butyric acid methyl ester/indium-tin oxide sandwich structure. The observed bipolar switching behavior can be attributed to the formation and dissolution of Ag filaments during positive and negative voltage sweeps, respectively. More importantly, conductance quantization with both integer and half integer multiples of single atomic point contact can be realized by slowing down the voltage sweep speed as well as by pulse measurement. The former may reflect the formed Ag filaments with different atomic point contacts, while the latter probably originates from the interaction between the Ag filaments and the elemental hydrogen provided by the organic storage medium. With appropriate current compliances, low resistance states with desired quantized conductance values are successfully achieved, thus showing the potential for ultrahigh density memory applications. Besides, 100 successive switching cycles with densely distributed resistance values of each resistance state and extrapolated retention properties over ten years are also demonstrated.