in our present endeavor. Finally, our present attempt is our modest first-step towards our central goal of establishing that these SUSP [*dual*]{} unitary operators are [*universal*]{} even in the case of [*non-Abelian*]{} theories.

The contents of our present investigation are organized as follows. In Sec. 2, we briefly discuss the (anti-)dual BRST symmetry transformations in the Lagrangian fromulation for the 1$D$ rigid rotor, modified versions of the 2$D$ Proca as well as anomalous gauge theories and 2$D$ self-dual bosonic field theory. We exploit the theoretical strength of the DHC and DGIRs to derive the above nilpotent symmetries within the framework of superfield formalism in Sec. 3. Our Sec. 4 deals with the derivation of the above nilpotent symmetries by using the SUSP [*dual*]{} unitary operators. In Sec. 5, we summarize our key results and point out a few future directions for further investigation.\
[*General Notations and Convention*]{}: We adopt the notation $s_{(a)d}$ for the on-shell as well as off-shell nilpotent (anti-)dual-BRST \[i.e. (anti-)co-BRST\] symmetry transformations for [*all*]{} the 1$D$ and 2$D$ models under consideration. In the description of 2$D$ theories, we choose 2$D$ flat Minkowski metric with the signature (+1, -1) so that the dot product between two non-null vectors 