  In this paper, we consider the Atkin-like polynomials that appeared in the
study of normalized extremal quasimodular forms of depth 1 on
$SL_{2}(\mathbb{Z})$ by Kaneko and Koike as orthogonal polynomials and clarify
their properties. By considering Atkin-like polynomials in terms of orthogonal
polynomials, we prove an unexpected connection between generalized Faber
polynomials, which are closely related to certain bases of the vector space of
weakly holomorphic modular forms, and normalized extremal quasimodular forms.
In particular, we show that the orthogonal polynomial expansion coefficients of
the generalized Faber polynomials by the Atkin-like polynomials appear in the
Fourier coefficients of normalized extremal quasimodular forms multiplied by
certain (weakly) holomorphic modular forms.
