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In this paper, we introduce new classes of functions defined within the open unit disk by integrating the concepts of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>λ</mi><mo>,</mo><mi>γ</mi><mo>)</mo></mrow></semantics></math></inline-formula>-symmetrical functions, generalized Janowski functions, and quantum calculus. We derive a structural formula and a representation theorem for the class <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi mathvariant="script">S</mi><mi>q</mi><mrow><mi>λ</mi><mo>,</mo><mi>γ</mi></mrow></msubsup><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. Utilizing convolution techniques and quantum calculus, we investigate convolution conditions supported by examples and corollary, establishing sufficient conditions. Additionally, we derive properties related to coefficient estimates, which further elucidate the characteristics of the defined function classes.