The main purpose of this paper is to define or create certain class \(Ch\left( { \alpha ,\beta ,\gamma ,A,B,\tau } \right),\) comprising of function interrelated with Chebyshiv polynomials. We introduce the coefficient bounds also presenting convolution property. Additionally through the utilization of structure of subordinations, two new subclasses \(M\left( {\alpha ,\beta ,\gamma ,A,B,\tau } \right) \; and \; N\left( {\lambda_{1} ,\lambda_{2} ,s} \right)\) of \(Ch\left( {\alpha ,\beta ,\gamma ,A,B,\tau } \right)\) are introduced and studied. For these subclasses, we obtain some properties such as coefficients estimate, extreme points, convexity property and geometric exegesis of inclusion outcomes are submitted. Furthermore, we demonstrate that under circumstances some restriction on parameters \(Ch\left( {\alpha ,\beta ,\gamma ,A,B,\tau } \right) = N\left( {\lambda_{1} ,\lambda_{2} ,s} \right).\) Chebyshev \( Ch\left( {\alpha ,\beta ,\gamma ,A,B,\tau } \right)\) polynomials provide a technique for constructing and investigating new classes of analytic univalent functions that are holomorphic and injective in a given domain. Geometric features of these functions, such as their starlikeness and convexity, are frequently studied since they are crucial in many different applications, such as conformal mapping and dynamic fluid dynamics.