J/ψ and open charm photoproduction on charm quarks in a proton via partonic subprocess γc → J/ψc are discussed based on the perturbative theory of quantum chromodynamics and nonrelativistic quark model. It is shown that the value and energy dependence of the cross-section for such process depend remarkably on the choice of charm distribution function in a proton. In the region of small z = EJ/Eγ < 0.2 the contribution of the γc → J/ψc subprocess in the inelastic J/ψ photoproduction spectra is larger than the contribution of the photon-gluon fusion subprocess. At the energy range of HERA collider charm quarks contribution in the total inclusive J/ψ photoproduction cross-section may be equal to 60% of the dominant contribution of photon-gluon fusion mechanism.