  We study the enhancement of the branching ratios of the decays $h \to \gamma
\gamma, \, \gamma Z$ in the Two Higgs Doublet Model Type III, assuming a
four-zero Yukawa Texture and a general Higgs potential. We show that these
processes are very sensitive to the flavor pattern of the Yukawa texture and
the structure of the triple coupling $h H^\pm H^\mp$ from the Higgs potential.
We can accomodate the parameters of the model such that one can obtain the $h
\to\gamma \gamma$ rates reported by the LHC and at the same time we can get a $
h \to \gamma Z$ fraction larger than in the SM and within experimental reach.
The possibility of obtaining a light charged Higgs boson within the ensuing
parameter space and compatible with current experimental measurements is also
presented.
