  We investigate open charm meson production in fixed-target LHCb experiment at
$\sqrt{s}=86.6$ GeV in $p+^4\!\mathrm{He}$ collisions. Theoretical calculations
of charm cross section are done in the framework of the $k_{T}$-factorization
approach. Its application in the kinematical range never examined before is
carefully discussed. We consider different schemes for the calculations
relevant for different unintegrated (transverse momentum dependent) parton
densities in a proton. We include in the analysis both CCFM- and DGLAP-based
models of unintegrated parton distributions appropriate for the considered
kinematics. Integrated as well as differential cross sections as a function of
$D^{0}$ meson rapidity and transverse momentum are shown and compared with the
experimental data. As a reference point, predictions of next-to-leading order
collinear approach are also presented and discussed. A very good agreement
between the experimental data and the $k_{T}$-factorization predictions was
obtained. Both the CCFM and the DGLAP-based frameworks for parton distributions
in a proton are successfully used to explain the LHCb fixed-target open charm
cross section.
