  We quantize the one-particle model of the ${\rm SU}(2|1)$ supersymmetric
multi-particle mechanics with the additional semi-dynamical spin degrees of
freedom. We find the relevant energy spectrum and the full set of physical
states as functions of the mass-dimension deformation parameter $m$ and ${\rm
SU}(2)$ spin $q \in \big( \mathbb{Z}_{>0}\,$, $1/2 + \mathbb{Z}_{\geqslant
0}\big)\,$. It is found that the states at the fixed energy level form
irreducible multiplets of the supergroup ${\rm SU}(2|1)\,$. Also, the hidden
superconformal symmetry ${\rm OSp}(4|2)$ of the model is revealed in the
classical and quantum cases. We calculate the ${\rm OSp}(4|2)$ Casimir
operators and demonstrate that the full set of the physical states belonging to
different energy levels at fixed $q$ are unified into an irreducible ${\rm
OSp}(4|2)$ multiplet.
