  We study quantum properties of SU$(2|1)$ supersymmetric (deformed ${\cal
N}=4$, $d=1$ supersymmetric) extension of the superintegrable
Smorodinsky--Winternitz system on a complex Euclidian space $\mathbb{C}^N$. The
full set of wave functions is constructed and the energy spectrum is
calculated. It is shown that SU$(2|1)$ supersymmetry implies the bosonic and
fermionic states to belong to separate energy levels, thus exhibiting the
"even-odd" splitting of the spectra. The superextended hidden symmetry
operators are also defined and their action on SU$(2|1)$ multiplets of the wave
functions is given. An equivalent description of the same system in terms of
superconformal SU$(2|1,1)$ quantum mechanics is considered and a new
representation of the hidden symmetry generators in terms of the SU$(2|1,1)$
ones is found.
