  We calculate the cross section for production of a soft photon and two hard
jets in the forward rapidity region in proton-nucleus collisions at high
energies. The calculation is performed within the hybrid formalism. The
hardness of the final particles is defined with respect to the saturation scale
of the nucleus. We consider both the correlation limit of small momentum
imbalance and the dilute target limit where the momentum imbalance is of the
order of the hardness of the jets. The results depend on the first two
transverse-momentum-dependent (TMD) gluon distributions of the nucleus.
