  Forward photoproduction of $J/\psi$ can be used to extract Generalized Parton
Distributions(GPD's) of gluons. We analyze the process at twist-3 level and
study relevant classifications of twist-3 gluon GPD's. At leading power or
twist-2 level the produced $J/\psi$ is transversely polarized. We find that at
twist-3 the produced $J/\psi$ is longitudinally polarized. Our study shows that
in high energy limit the twist-3 amplitude is only suppressed by the inverse
power of the heavy quark mass relatively to the twist-2 amplitude. This
indicates that the power correction to the cross-section of unpolarized
$J/\psi$ can have a sizeable effect. We have also derived the amplitude of the
production of $h_c$ at twist-3, but the result contains end-point
singularities. The production of other quarkonia has been briefly discussed.
