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The main objective of this paper is to study a new family of analytic functions that are <i>q</i>-starlike with respect to <i>m</i>-symmetrical points and subordinate to the <i>q</i>-Janowski function. We investigate inclusion results, sufficient conditions, coefficients estimates, bounds for Fekete–Szego functional <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>|</mo><msub><mi>a</mi><mn>3</mn></msub><mo>−</mo><mi>μ</mi><msubsup><mi>a</mi><mrow><mn>2</mn></mrow><mn>2</mn></msubsup><mo>|</mo></mrow></semantics></math></inline-formula> and convolution properties for the functions belonging to this new class. Several consequences of main results are also obtained.