This research paper introduces the novel subclass of bi‐univalent functions that are connected to Fibonacci numbers. Our main contributions in this study involve establishing constraints on the absolute values of the second coefficient |a2| and the third coefficient |a3| for functions within this specific subclass. In addition, we provide solutions to Fekete–Szegö functional problems. Furthermore, our investigation reveals intriguing outcomes resulting from the specific parameter values used in our main findings.