Deformed supersymmetric quantum mechanics with spin variables

We quantize the one-particle model of the $\mathrm{S}\mathrm{U}(2\mathrm{\mid }1)$ 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 $\mathrm{S}\mathrm{U}(2\mathrm{\mid }1)$. Also, the hidden superconformal symmetry $\mathrm{O}\mathrm{S}\mathrm{p}(4\mathrm{\mid }2)$ of the model is revealed in the classical and quantum cases. We calculate the $\mathrm{O}\mathrm{S}\mathrm{p}(4\mathrm{\mid }2)$ 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.