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In 1999, for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mn>0</mn><mo>≤</mo><mi>k</mi><mo><</mo><mo>∞</mo><mo>)</mo></mrow></semantics></math></inline-formula>, the concept of conic domain by defining <i>k</i>-uniform convex functions were introduced by Kanas and Wisniowska and then in 2000, they defined related <i>k</i>-starlike functions denoted by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>k</mi><mo>−</mo><mi>U</mi><mi>C</mi><mi>V</mi></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>k</mi><mo>−</mo><mi>S</mi><mi>T</mi></mrow></semantics></math></inline-formula> respectively. Motivated by their studies, in our work, we define the class of <i>k</i>-parabolic starlike functions, denoted <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>k</mi><mo>−</mo><msub><mi mathvariant="script">S</mi><mrow><msub><mi mathvariant="script">H</mi><mi>m</mi></msub><mo>,</mo><mi>q</mi></mrow></msub></mrow></semantics></math></inline-formula>, by using quasi-subordination for <i>m</i>-fold symmetric analytic functions, making use of conic domain <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mo>Ω</mo><mi>k</mi></msub></semantics></math></inline-formula>. We determine the coefficient bounds and estimate Fekete–Szegö functional by the help of <i>m</i>-th root transform and quasi subordination for functions belonging the class <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>k</mi><mo>−</mo><msub><mi mathvariant="script">S</mi><mrow><msub><mi mathvariant="script">H</mi><mi>m</mi></msub><mo>,</mo><mi>q</mi></mrow></msub></mrow></semantics></math></inline-formula>.