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In this paper, we discussed a new subclass <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mrow><mi mathvariant="script">J</mi><mi mathvariant="script">Q</mi></mrow><mrow><mo>⅁</mo><mo>,</mo><mi>A</mi></mrow><mi>B</mi></msubsup><mrow><mo>(</mo><mi>q</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> of bi-univalent functions in the unit disk <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">U</mi></semantics></math></inline-formula> using <i>q</i>-generalized Janowski function and <i>q</i>-derivative. Additionally, certain properties were examined and effectively demonstrated, such as the second Hankel determinant, Fekete–Szegö estimates, and Coefficients Bounds. Each of these bounds were precise and were confirmed by finding the extremal function for the new class. Furthermore, there are in-depth conversations available regarding certain intriguing specific cases of the outcomes achieved.