  We propose an extended 2HDM with $Q_6\times Z_4\times Z_2$ symmetry that can
interpret the SM fermion mass hierarchy and their mixing patterns with the
Dirac CP phase in the framework of the type-I seesaw mechanism. The smallness
of neutrino masses is obtained via the Type-I seesaw mechanism. Both normal and
inverted neutrino mass hierarchies are consistent with the experimental data on
the lepton and quark masses and mixing patterns. The prediction for the Dirac
phase is $\delta_{CP}\in (1.50, 1.82)\pi$ for normal ordering and
$\delta_{CP}\in (1.50, 1.80)\pi$ for inverted ordering that includes its
experimentally maximum value. The sum of neutrino masses is predicted to be
$\sum m_i \in (58.50, 60.50)$\, meV for normal ordering and $\sum m_i\in
(98.50, 101.00)\, $ \, meV for inverted ordering which are well consistent with
all the recent limits. In addition, the predictions for the effective neutrino
masses are $\langle m_{ee}\rangle \in (3.70, 3.90)$\, meV for normal ordering
and $\langle m_{ee}\rangle \in (48.00, 49.40)$\, meV for inverted ordering
which are in consistence with the recent experimental bounds. For the quark
sector, the derived results are also in agreement with the recent data on the
quark masses and mixing angles. The considered model can also accommodate the
muon anomalous magnetic moment and the mesons oscillation in accordance with
the experiment data.
