We demonstrate for the first time, to the best of our knowledge, the fabrication of high-Q crystalline optical microresonators from cubic yttria-stabilized zirconia (YSZ). Intrinsic Q factors up to 80 million are obtained, indicating an upper bound absorption coefficient of 0.001cm-1 for YSZ crystals at the telecom wavelength. Through laser-scanned spectroscopy on a few-mode YSZ microresonator with a radius of 300 μm, we find that the mode crossing effect in the case of weak coupling can induce a repelling disruption of free spectral range values between transverse mode families. Generation of soliton and soliton crystals in such a YSZ microcomb platform operated in the normal dispersion regime is observed. A breathing comb behavior is also reported. Our finding has enriched comb generation platforms with potential multidisciplinary capabilities linked to properties of YSZ crystals in superconducting films and sensors.