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We investigate a consistent scenario of time-varying neutrino masses, and discuss its impact on cosmology, beta decay, and neutrino oscillation experiments. Such time-varying masses are assumed to be generated by the coupling between a sterile neutrino and an ultralight scalar field, which in turn affects the light neutrinos by mixing. Besides, the scalar could act as an ultralight dark matter candidate. We demonstrate how various cosmological bounds, such as those coming from Big Bang nucleosynthesis, the cosmic microwave background, as well as large scale structures, can be evaded in this model. This scenario can be further constrained using multiple terrestrial experiments. In particular, for beta-decay experiments like KATRIN, non-trivial distortions to the electron spectrum can be induced, even when time-variation is fast and gets averaged out. Furthermore, the presence of time-varying masses of sterile neutrinos will alter the interpretation of light sterile neutrino parameter space in the context of the reactor and gallium anomalies. In addition, we also study the impact of such time-varying neutrino masses on results from the BEST collaboration, which have recently strengthened the gallium anomaly. If confirmed, we find that the time-varying neutrino mass hypothesis could give a better fit to the recent BEST data.