  In this communication, we present the results of the Five-fold Differential
Cross Section (5DCS) and Triple Differential Cross Section (TDCS) for the
(e,2e) process on molecular hydrogen ($H_2$) by the plane wave and the twisted
electron beam impact. The formalism is developed within the first Born
approximation using the plane wave and the twisted wave for the incident
electron beam. We describe the plane wave, Heitler-London type wave function
and Coulomb wave for the scattered electron, $H_2$ molecular state, and the
ejected electron respectively. We compare the angular profiles of the 5DCS and
TDCS for the different values of Orbital Angular Momentum (OAM) number {\it m}
of the twisted electron beam with that of the plane wave beam. We also present
the 5DCS for different molecular orientations and study the effect of {\it m}
on the 5DCS. We further investigate the influence of the twisted electron beam
on the (e,2e) process on the $H_2$ molecule from the perspective of the
"Young-type" interference of the scattered waves, emanating from the two atomic
centers of the $H_2$ molecule. We also study the TDCS for macroscopic $H_2$
target to explore the effect of opening angle ($\theta_p$) of the twisted
electron beam on the TDCS. Our results clearly show the effect of the twisted
electron's OAM number (m) and the opening angle ($\theta_p$) on the 5DCS and
TDCS of the molecular hydrogen.
