In a paper they write once, $(\mathbb{Z}_n^*)^2$. Is this the group of quadratic residues or is it something else?

Here the theorem:

Under the strong RSA assumption, given a modulus $n$, along with random elements $g, h \in (\mathbb{Z}_n^∗)^2$, it is hard to compute $w in \mathbb{Z}_n^*$ and integers $a, b, c$ such that $w^c = g^a h^b$ and ($c \nmid a$ or $c \nmid b$).