  Chiral symmetry breaking comes from the mass dynamically generated through
interaction of Dirac fermions for both quantum electrodynamics in (2+1)D (QED3)
and (3+1)D (QED4). In QED3, the presence of a Chern-Simons (CS) parameter
affects the critical structure of the theory, favoring the symmetric phase
where the electron remains massless. Here, we calculate the main effects of a
Pseudo-Chern-Simons (PCS) parameter $\theta$ into the dynamical mass generation
of Pseudo quantum electrodynamics (PQED). The $\theta$-parameter provides a
mass scale for PQED at classical level and appears as the pole of the
gauge-field propagator. After calculating the full electron propagator with the
Schwinger-Dyson equation at quenched-rainbow and large-$N$ approximations, we
conclude that $\theta$ affects the critical parameters related to the
fine-structure constant, $\alpha_c(\theta)$, and to the number of copies of the
matter field, $N_c(\theta)$, by favoring the symmetric phase. In the continuum
limit ($\Lambda\to \infty$), nevertheless, the $\theta$-parameter do not affect
the critical parameters. We also compare our analytical results with numerical
findings of the integral equation for the mass function of the electron.
