  The normalization of the leading-twist photon distribution amplitude (DA),
$f_{\gamma}^{\perp}$, is an important ingredient in the study of exclusive
processes involving the photon emission by means of QCD sum-rules. In this
paper we determine the up- , down- and strange-quark contribution to
$f_{\gamma}^{\perp}$ by exploiting its relation to the zero-momentum two-point
correlation function of the electromagnetic current $J_{\rm em}^{\mu}$ and the
electric component of the tensor current $T^{\mu\nu}$. To that end we employ
the gauge ensembles obtained by using $N_{f}=2+1+1$ Wilson-Clover twisted-mass
quark flavors, generated by the Extended Twisted Mass (ETM) Collaboration, and
after adding all sources of systematic uncertainties, we obtain a total error
of $1.5\%$ and $3.5\%$, respectively, for the light- ($u$ and $d$) and
strange-quark contribution to $f_{\gamma}^{\perp}(2~{\rm GeV})$ in the
$\overline{\mathrm{MS}}$ scheme, thus improving their accuracy by a factor of
$2.3$ and $2.8$, respectively. For the strange-quark contribution
$f_{\gamma,s}^{\perp}(2~{\rm GeV})$, we observe a discrepancy with respect to
previous lattice calculations. By combining our result with the world average
lattice value of the chiral condensate, we obtain for the susceptibility of the
quark condensate $\chi_d^{\overline{\mathrm{MS}}} (2\, {\rm GeV}) \simeq
\chi_u^{\overline{\mathrm{MS}}} (2\, {\rm GeV}) =2.17(12)~{\rm GeV^{-2}}$.
