  We obtain exact solutions of the (2+1) dimensional Dirac oscillator in a
homogeneous magnetic field within the Anti-Snyder modified uncertainty relation
characterized by a momentum cut-off ($p\leq p_{\text{max}}=1/ \sqrt{\beta}$).
In ordinary quantum mechanics ($\beta\to 0$) this system is known to have a
single left-right chiral quantum phase transition (QPT). We show that a finite
momentum cut-off modifies the spectrum introducing additional quantum phase
transitions. It is also shown that the presence of momentum cut-off modifies
the degeneracy of the states.
