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UCoGe is reported as a weak ferromagnetic (FM) two-band superconductor (SC)with the critical temperature, $T_{\mathrm{SC}}\sim$ 0.7 K and the Curietemperature, $T_{\mathrm{C}}\sim$ 3 K at ambient pressure. We report exoticattributes of the SC and FM state in moderate magnetic fields. The observedphenomena clearly demonstrate that the SC regime is superior to theparamagnetic state in the vicinity of $T_{\mathrm{SC}}$. Above$T_{\mathrm{SC}}$, the zero-field state is characterized by a regime withstrong FM spin fluctuations, suggesting proximity of the FM quantum criticalpoint (FM-QCP). In addition, we observed that the robust SC regime developsindependently on the existence or lack of the long-range FM ordering.

Crossover between SC states in an unconventional superconductor UCoGe driven by ferromagnetic spin fluctuations