  In a previous paper, the first and third authors gave an explicit realization
of the geometric Langlands correspondence for hypergeometric sheaves,
considered as $\textrm{GL}_n$-local systems. Certain hypergeometric local
systems admit a symplectic or orthogonal structure, which can be viewed as
$\check{G}$-local systems, for a classical group $\check{G}$. This article aims
to realize the geometric Langlands correspondence for these $\check{G}$-local
systems. We study this problem from two aspects. In the first approach, we
define the hypergeometric automorphic data for a classical group $G$ in the
framework of Yun, one of whose local components is a new class of euphotic
representations in the sense of Jakob-Yun. We prove the rigidity of
hypergeometric automorphic data under natural assumptions, which allows us to
define $\check{G}$-local systems $\mathcal{E}_{\check{G}}$ on $\mathbb{G}_m$ as
Hecke eigenvalues (in both $\ell$-adic and de Rham setting). In the second
approach (which works only in the de Rham setting), we quantize an enhanced
ramified Hitchin system, following Beilinson-Drinfeld and Zhu, and identify
$\mathcal{E}_{\check{G}}$ with certain $\check{G}$-opers on $\mathbb{G}_m$.
Finally, we compare these $\check{G}$-opers with hypergeometric local systems.
