very useful relationships (see, e.g. \[18\] for details) $$\begin{aligned}
&&\partial \cdot R^{(1)}\,=\,\partial \cdot R^{(2)}\,=\,\partial \cdot S \,=\,0, \quad 
s\,=\,\bar s\,=\,0, \\ \nonumber
&&B_{1}\,=\,B_{4}\,=\,0,\quad B_{2}\,+\,B_{3}\,=\,0,\end{aligned}$$ where the relation $B_{2}\,+\,B_{3}\,=\,0$ is like the CF-type condition which turns out to be a [*trivial*]{} relationship. We would like to state that the details of the equation (24) have been worked out in our earlier work on the superfield approach to the modified version of 2$D$ Proca theory \[18\]. The interesting point is that the above conditions are true in the AVSF approach to the modified version of 2$D$ anomalous gauge theory, too.

The above relations do [*not*]{} lead to the exact form of $R_{\mu}^{(1)}, R_{\mu}^{(2)}, S_{\mu}$ and ($B_{2}, B_{3}$). The CF-type condition $B_{2}\,+\,B_{3}\,=\,0$ allows us to choose $B_{2}\,=\,\cal B$ so that $B_{3}\,=\,-\,\cal B$. Now, we exploit the virtue of the AVSF to derive the [*exact*]{} forms of the secondary fields and observe that the following (anti-)co-BRST invariant quantity $$\begin{aligned}
s_{(a)d}\,\Big[\varepsilon^{\mu\nu}\,(\partial_{\mu}{\cal B)}\,A_{\nu}\,
-\,i\,\partial_{\mu}\,\bar C \partial^{\mu} C\Big]\,=\,0,\end{aligned}$$ permits us to demand that the superfield generalization of the above quantity on the (2, 2)-dimensional supermanifold must be independent of the soul co-ordinates ($\theta, \bar\theta$). Thus, we have the following equality $$\begin{aligned}
\varepsilon^{\mu\nu}\,\bigl (\partial_{\mu}{\cal B} (x) \bigr )\,{\cal 