  In this paper, we consider Galois representations of the absolute Galois
group $\text{Gal}(\overline {\mathbb Q}/\mathbb Q)$ attached to modular forms
for noncongruence subgroups of $\text{SL}_2(\mathbb Z)$. When the underlying
modular curves have a model over $\mathbb Q$, these representations are
constructed by Scholl and are referred to as Scholl representations, which form
a large class of motivic Galois representations. In particular, by a result of
Belyi, Scholl representations include the Galois actions on the Jacobian
varieties of algebraic curves defined over $\mathbb Q$. As Scholl
representations are motivic, they are expected to correspond to automorphic
representations according to the Langlands philosophy. Using recent
developments in the automorphy lifting theorem, we obtain various automphy and
potential automorphy results for potentially $\text{GL}_2$-type Galois
representations associated to noncongruence modular forms. Our results are
applied to various kinds of examples. Especially, we obtain potential
automorphy results for Galois representations attached to an infinite family of
spaces of weight 3 noncongruence cusp forms of arbitrarily large dimensions.
