  The Pauli equation, an important equation of quantum mechanics, allows us to
study the dynamics of spin-$1/2$ particles. The Dunkl derivative, when used
instead of the ordinary derivative, leads to obtaining parity-dependent
solutions. Motivated by these facts, in this work, we consider a
two-dimensional nonrelativistic spin-$1/2$ particle system in the presence of
an external magnetic field, and we investigate its parity-dependent dynamics by
solving the Pauli equation analytically. Next, we assume the system to be in
thermal equilibrium, and we examine various thermal quantities of the system.
