  This paper is devoted to studying the multiple recurrent property of
topologically mildly mixing systems along generalized polynomials. We show that
if a minimal system is topologically mildly mixing, then it is mild mixing of
higher orders along generalized polynomials. Precisely, suppose that $(X, T)$
is a topologically mildly mixing minimal system, $d\in \mathbb{N}$, $p_1,
\dots, p_d$ are integer-valued generalized polynomials with $(p_1, \dots, p_d)$
non-degenerate. Then for all non-empty open subsets $U , V_1, \dots, V_d $ of
$X$, $$\{n\in \Z: U\cap T^{-p_1(n) }V_1 \cap \dots \cap T^{-p_d(n) }V_d \neq
\emptyset \}$$ is an IP$^*$-set.
