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