  Electronic transport in the $\alpha-\mathcal{T}_3$ model of pseudospin-1
fermions with a finite gap is studied within the semiclassical Boltzmann
approximation. We show that coupling of the orbital magnetic moment to the
external magnetic field, which is otherwise absent in the massless model,
breaks valley symmetry, results in finite and measurable corrections to the
longitudinal and Hall conductivity, and yields anomalous Hall conductivity due
to the Berry curvature. We also show that, remarkably, magnetoresistance
induced by the orbital magnetic moment can be either positive or negative; the
sign depends on the amount of disorder, and is different for both conventional
and anomalous contributions to the magnetoresistance. Recent material advances
and upcoming experiments on cold atoms that may realize pseudospin-1 fermions
makes our study timely and appropriate.
