  We study the superconducting proximity effect in an InAs nanowire contacted
by Ta-based superconducting electrodes. Using local bottom gates, we control
the potential landscape along the nanowire, tuning its conductance to a
quasi-ballistic regime. At high magnetic field ($B$), we observe approximately
quantized conductance plateaus associated with the first two spin-polarized
one-dimensional modes. For $B < 1$ T, the onset of superconductivity occurs in
concomitance with the development of sizeable charge localization leading to a
0.7-type conductance anomaly. In this regime, the proximity supercurrent
exhibits an unusual, non-monotonic $B$ dependence. We interpret this finding in
terms of a competition between the Kondo effect, dominating near $B=0$, and the
Zeeman effect, enforcing spin polarization and the emergence of a $\pi$ phase
shift in the Josephson relation at higher $B$.

Mesoscale and Nanoscale Physics