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The electronic states on a finite width $\alpha-\mathcal{T}_3$ ribbon in amagnetic field are studied in the framework of low-energy effective theory.Both zigzag and armchair types of boundary conditions are analyzed. Theanalytical solutions are compared with the results of numerical tight-bindingcalculations. It is found that the flat band of zero energy survives for alltypes of boundary conditions. The analytical estimates for the spectral gap ina weak magnetic field are discussed. For zigzag type boundary conditions theapproximate expressions for the edge and bulk electron states in the strongmagnetic field are found.

Electronic states of pseudospin-1 fermions in $\alpha-\mathcal{T}_3$ lattice ribbons in a magnetic field