Establishing relations between fundamental effects in far-flung areas of physics is a subject of great interest in the current research. Realization of a novel photonic system akin to the radio-frequency superconducting quantum interference device (RF-SQUID), in a fiber laser cavity with epsilon-near-zero (ENZ) nanolayers as intra-cavity components is reported here. Emulating the RF-SQUID scheme, the photonic counterpart of the supercurrent, represented by the optical wave, circulates in the cavity, passing through effective optical potential barriers. Different ENZ wavelengths translate into distinct spectral outputs through the variation of cavity resonances, emulating the situation with a frequency-varying tank circuit in the RF-SQUID. Due to the presence of the ENZ element, the optical potential barrier is far lower for selected frequency components, granting them advantage in the gain-resource competition. The findings reported in this work provide a deeper insight into the ultrafast ENZ photonics, revealing a new path toward the design of nanophotonic on-chip devices with various operational functions, and offer a new approach to study superconducting and quantum-mechanical systems.