  The semi-inclusive electroproduction of exotic hadrons, including the
$T_{cc}$, $P_{cs}$, and hidden-charm baryon-antibaryon states, is explored
under the assumption that they are $S$-wave hadronic molecules of a pair of
charmed hadrons. We employ the Monte Carlo event generator Pythia to produce
the hadron pairs and then bind them together to form hadronic molecules. With
the use of such a production mechanism, the semi-inclusive electroproduction
rates are estimated at the order-of-magnitude level. Our results indicate that
a larger number of $P_{cs}$ states and $\Lambda_c\bar{\Lambda}_c$ molecules can
be produced at the proposed electron-ion colliders in China (EicC) and in the
US (EIC). The results also suggest that the $T_{cc}$ states and other
hidden-charm baryon-antibaryon states can be searched for at EIC. Besides, the
potential 24-GeV upgrade of the Continuous Beam Accelerator Facility at the
Thomas Jefferson National Accelerator Facility can play an important role in
the search for the hidden-charm tetraquark and pentaquark states due to its
high luminosity.
