  We study the production, in Deep Inelastic Scattering at high energy, of a
quark-gluon dijet induced by $t$-channel quark exchange with the target, which
goes beyond the eikonal approximation. Throughout this study we follow the
Color Glass Condensate approach, keep full dependence on the quark mass and
consider the target to be unpolarized. We focus on the correlation limit in
which the produced jets fly almost back-to-back and find a factorized
expression for the cross section, for both longitudinal and transverse photons,
involving the unpolarized quark transverse momentum dependent distribution.
Quark-gluon dijets can be distinguished from other types of dijets at least in
the heavy quark case, thanks to heavy flavor tagging. In that case, the
dominant background is expected to come from the eikonal production of a
quark-antiquark-gluon system. We propose experimental cuts to suppress that
background contribution, making the process of quark-gluon dijet production in
Deep Inelastic Scattering a new method to probe the quark transverse momentum
dependent distribution at the Electron Ion Collider.
