  We investigate quantum transport through a rectangular potential barrier in
Weyl semimetals (WSMs) and multi-Weyl semimetals (MSMs), within the framework
of Landauer-B\"uttiker formalism. Our study uncovers the role of nodal topology
imprinted in the electric current and the shot noise. We find that, in contrast
to the finite odd-order conductance and noise power, the even-order
contributions vanish at the nodes. Additionally, depending on the topological
charge ($J$), the linear conductance ($G_1$) scales with the Fermi energy
($E_F$) as $G_1^{E_F>U}\propto E_F^{2/J}$. We demonstrate that the
$E_F$-dependence of the second-order conductance and shot noise power could
quite remarkably distinguish an MSM from a WSM depending on the band topology,
and may induce several smoking gun experiments in nanostructures made out of
WSMs and MSMs. Analyzing shot noise and Fano factor, we show that the transport
across the rectangular barrier follows the sub-Poissonian statistics.
Interestingly, we obtain universal values of Fano factor at the nodes unique to
their topological charges. The universality for a fixed $J$, however, indicates
that only a fixed number of open channels participate in the transport through
evanescent waves at the nodes. The proposed results can serve as a potential
diagnostic tool to identify different topological systems in experiments.
