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We study the group velocities of electronic states and distributions ofcurrents in $\alpha-\mathcal{T}_3$ lattice ribbons under a uniformperpendicular magnetic field. Using the effective low-energy model we analyzeall possible simple configurations of lattice termination with zigzag andarmchair boundaries. We show that the edge current depends on the type ofzigzag termination, and can be zero or finite near the edge. Also similardependence is observed in the case of armchair termination and is related tothe size of the ribbon. The nonzero current flowing along the edge can be useda signature of formation of propagating edge states. Also we show thequalitative difference in the distribution of the edge current between the caseof $\alpha=1$ (dice model) and other values of model parameter $\alpha\neq 1$for armchair-terminated ribbons.

Current distribution and group velocities for electronic states on $\alpha-\mathcal{T}_3$ lattice ribbons in a magnetic field