In this work, we describe and investigate a novel class of analytic functions, including the new functions and the Bazilevič functions. Bazilevič functions are a crucial part of analytic functions and have many applications in pure and applied mathematics. We focus on constructing Toeplitz matrices, studying their structural properties, and assessing their eigenvalues and trends for this class of functions. The goal of this work is to calculate coefficient estimates for the functions in this family for the Toeplitz matrix’s first four determinants, symmetric T2 (2), T2 (3), T3 (1), and T3 (2).