Energy-efficient cryogenic memory systems play a critical role in a wide spectrum of applications focused on ultra-energy-efficient information and communication technologies, such as quantum computing or superconducting electronics. Neuromorphic systems, known for their superior energy efficiency, have emerged as a promising approach for in-memory computing. Specifically, strongly correlated oxides that exhibit Mott metal-insulator transitions through field-induced oxygen movement are of great interest for analog memory and neuromorphic computing. Yet, optimizing their performance at low temperatures may prove challenging due to their reliance on ionic motion. In this study, superconducting structures composed of strongly correlated YBa2Cu3O7 - x (YBCO) combined with ferromagnetic La0.7Sr0.3MnO3 (LSMO) are investigated to obtain non-volatile multilevel memristive switching effects with high performance at cryogenic temperatures. This research reveals the presence of two competing switching mechanisms, which are attributed to the movement of oxygen vacancies and electric carriers within these structures. It is determined that a phase transition induced by the movement of holes is the primary factor influencing the switching dynamics at low temperatures. Additionally, a physics-based compact model is proposed that accurately replicates the experimental findings and provides a tool for circuit-level design.