  We introduce a class of four dimensional field theories constructed by
quotienting ordinary $\mathcal{N}=4$ $U(N)$ SYM by particular combinations of
R-symmetry and $SL(2,\mathbb{Z})$ automorphisms. These theories appear
naturally on the worldvolume of D3 branes probing terminal singularities in
F-theory, where they can be thought of as non-perturbative generalizations of
the O3 plane. We focus on cases preserving only 12 supercharges, where the
quotient gives rise to theories with coupling fixed at a value of order one.
These constructions possess an unconventional large $N$ limit described by a
non-trivial F-theory fibration with base $AdS_5\times (S^5/\mathbb{Z}_k)$. Upon
reduction on a circle the $\mathcal{N}=3$ theories flow to well-known
$\mathcal{N}=6$ ABJM theories.
