  We study four-dimensional superconformal field theories living on the
worldvolume of $D3$ branes probing minimally-supersymmetric F-theory
backgrounds, focusing on the case of orbi-orientifold setups with and without
7-branes. We observe that these theories are closely related to
compactifications of six-dimensional $\mathcal{N}=(1,0)$ theories on a torus
with flux, where the flux quanta is mapped in Type IIB to the defining data of
the orbifold group. We analyze the cases of class $\mathcal{S}_k$ theories as
well as of compactifications of the E-string and of orbi-instanton theories. We
also classify $\mathcal{S}$-fold configurations in F-theory preserving minimal
supersymmetry in four dimensions and their mass deformations.
