  In the presence of external off-resonance and circularly-polarized
irradiation, we have derived a many-body formalism and performed a detailed
numerical analysis for both the conduction and optical currents in
$\alpha-\mc{T}_3$ lattices. The calculated complex many-body dielectric
function, as well as conductivities of displacement and transport currents,
display strong dependence on the lattice-structure parameter $\alpha$,
especially approaching the graphene limit with $\alpha \to 0$. Unique features
in dispersion and damping of plasmon modes are observed with different $\alpha$
values, which are further accompanied by a reduced transport conductivity under
irradiation. The discovery in this paper can be used for designing novel
multi-functional nanoelectronic and nanoplasmonic devices.
