  Despite the popularity of two-Higgs-doublet models (2HDMs) with a gauged
abelian flavor symmetry, the allowed Yukawa textures have only been partly
explored so far. In this work, we classify and compare every anomaly-free
instance, in the case of having two generations of right-handed neutrinos and a
type-I seesaw mechanism. We found 16 valid implementations in total, out of
which 11 agree well with current experimental bounds. To our knowledge, neither
of these models have been considered previously.
