Memristors, owing to their uncomplicated structure and resemblance to biological synapses, are predicted to see increased usage in the domain of artificial intelligence. Additionally, to augment the capacity for multilayer data storage in high-density memory applications, meticulous regulation of quantized conduction with an extremely low transition energy is required. In this work, an a-HfSiOx-based memristor was grown through atomic layer deposition (ALD) and investigated for its electrical and biological properties for use in multilevel switching memory and neuromorphic computing systems. The crystal structure and chemical distribution of the HfSiOx/TaN layers were analyzed using X-ray diffraction (XRD) and X-ray photoelectron spectroscopy (XPS), respectively. The Pt/a-HfSiOx/TaN memristor was confirmed by transmission electron microscopy (TEM) and showed analog bipolar switching behavior with high endurance stability (1000 cycles), long data retention performance (104s), and uniform voltage distribution. Its multilevel capability was demonstrated by restricting current compliance (CC) and stopping the reset voltage. The memristor exhibited synaptic properties, such as short-term plasticity, excitatory postsynaptic current (EPSC), spiking-rate-dependent plasticity (SRDP), post-tetanic potentiation (PTP), and paired-pulse facilitation (PPF). Furthermore, it demonstrated 94.6% pattern accuracy in neural network simulations. Thus, a-HfSiOx-based memristors have great potential for use in multilevel memory and neuromorphic computing systems.Graphical AbstractSupplementary InformationThe online version contains supplementary material available at 10.1186/s40580-023-00380-8.