  In the framework of the model motivated by perturbative calculations in the
fourth $O(\alpha^3_s\alpha)$-order, the estimates for the $\gamma p$
cross-section of the $D^*$-meson production in the ZEUS experiment are
performed. We factorize the hadronization of $(c\bar q)$-state hardly produced
in perturbative QCD, which allows us to take into account the higher twist
terms in the powers of $1/p_T$ at $p_T\sim m_c$ and to correctly reproduce the
c-quark fragmentation dominant at high $p_T\gg m_c$ to the given order of
$\alpha_s$. We find a good agreement with the experimental data on the
photoproduction, if the color-octet $(c\bar q)$-state is taken into account,
which yields $<O_{(8)} > \approx 0.33-0.49 GeV^3$.
