  Recent studies have shown that the use of Dunkl derivatives instead of
ordinary derivatives leads to deriving parity-dependent dynamic solutions.
According to this motivation in this manuscript, we formulate the
Dunkl-Schr\"odinger equation within the position-dependent mass formalism and
derive an algebraic solution out of it. Our systematic approach lets us observe
some new findings in addition to the earlier ones. For example, we find that
the solution of the Dunkl-Schr\"oodinger equation with position-dependent mass
cannot be considered independent of the choice of parameters. Similarly,
through the sl(2) algebra, the energy spectrum and the corresponding wave
functions are derived in terms of possible Dunkl, ($\mu$), and mass,
($\alpha$), parameters.
