  We have examined the production of J/$\psi$ mesons in high energy
proton-proton and proton-nucleus collisions at beam energies in the range from
158 GeV to 920 GeV, available from different fixed target experiments. In the
employed model J/$\psi$ production in hadronic collisions is assumed to be a
factorisable two step process: (i) production of a $c\bar{c}$ pair which can be
reliably described by perturbative QCD, and (ii) formation of J/$\psi$
resonance from the $c\bar{c}$ pair, which can be conveniently parameterized
incorporating different existing physical mechanisms of color neutralization.
We show that, for lower collision energies, J/$\psi$ production through
quark-anti-quark annihilation gives larger contribution at higher $x_F$, while
gluon-gluon fusion dominates the production at smaller $x_F$. For
proton-nucleus collisions the model takes into account both the initial state
modification of parton distributions in nuclei and the final state interaction
of the produced $c\bar{c}$ pairs with the target nucleons. The model is found
to give reasonable description of data on J/$\psi$ production in protonic and
proton-nucleus collisions, for different existing fixed target experiments. In
case of proton-nucleus collisions, our calculations show a non-negligible
dependence of the final state nuclear dissociation of J/$\psi$ mesons on the
energy of the incident proton beam. The model has been applied to predict the
J/$\psi$ production and suppression expected in proton-nucleus collisions at
energies relevant to FAIR, the upcoming accelerator facility at Darmstadt,
Germany. The amount of suppressions, for different mechanisms of J/$\psi$
hadronization has been found to be distinguishably different which might help
an experimental settlement of the much controversial issue of color
neutralization.
