  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 Curie
temperature, $T_{\mathrm{C}}\sim$ 3 K at ambient pressure. We report exotic
attributes of the SC and FM state in moderate magnetic fields. The observed
phenomena clearly demonstrate that the SC regime is superior to the
paramagnetic state in the vicinity of $T_{\mathrm{SC}}$. Above
$T_{\mathrm{SC}}$, the zero-field state is characterized by a regime with
strong FM spin fluctuations, suggesting proximity of the FM quantum critical
point (FM-QCP). In addition, we observed that the robust SC regime develops
independently on the existence or lack of the long-range FM ordering.
