In this paper, we investigate the properties of functions belonging to the classes $\psi (\eta )\in {\overline{\mathcal{T}}}_q^{j,k}(A,B)$ and $\psi (\eta )\in {\overline{\mathcal{K}}}_q^{j,k}(A,B)$, these functions are defined within the context of $q$-calculus and $(j,k)$-symmetrical functions. We employ convolution techniques and quantum calculus to explore the convolution conditions, which will serve as foundational results for further studies in our work Furthermore, we establish conditions for membership in $\psi (\eta )\in {\overline{\mathcal{T}}}_q^{j,k}(A,B)$ and present an example demonstrating the application of these results to rational functions.