Quasi-subordination which is an extension of the majorization and subordination principle, has been used to define a subclass of Bazilevič functions of complex order. Various classes of analytic functions that map unit disc onto conic domains and some classes of special functions are studied in dual. Inequalities for the initial Taylor-Maclaurin coefficients and unified solution of Fekete-Szegö problem for subclasses of analytic functions related to various conic regions are our main results. Our main results have many applications which are presented in the form of corollaries. © 2021 the Author(s), licensee AIMS Press.