  The recent introduction of a deformed non-minimal version of the
noncommutative Standard Model in the enveloping-algebra approach, having a
one-loop renormalisable gauge sector involving a higher order gauge term,
motivates us to consider the possibility of extending the fermion sector with
additional deformations, i.e. higher order fermionic terms. Since the
renormalisability properties of the fermion sector of the model are not yet
fully known, we work with an effective fermion lagrangian which includes
noncommutative higher order terms involving a contraction with the
noncommutative $\theta$ tensor aside from the star products, so that these
terms annihilate in the commutative limit. Some of these terms violate CPT in
the weak sector, and some violate CP in the strong and hypercharge sectors. We
apply this framework to the reevaluation of the decay rates of quarkonia
(\bar{q}q_{1} = J/\psi, \Upsilon) into two photons. These decays, which are
forbidden in the ordinary Standard Model, had been previously studied as
possible signals for noncommutativity, but not in the framework of the better
behaved deformed non-minimal version of the noncommutative Standard Model. Weak
CPT or strong-hypercharge CP violating interactions do not contribute to the
result. If the parameters of the model take natural values, for the vast
majority of configurations the resulting branching ratios are enhanced with
respect to their values in the minimal version of the noncommutative Standard
Model. Also for more than half of the parameter space, the rates are larger
than the maximal rates that were calculated in the undeformed version of the
non-minimal noncommutative Standard Model. Tuning the dimensionless parameters
the predicted branching ratios can fall within the current experimental bounds.
