We predict the occurrence of Bose-Einstein condensation and superfluidity of dipolar magnetoexcitons for a pair of quasi-two-dimensional spatially separated $alpha$-${cal T}_3$ layers. We have solved a two-body problem for an electron and a hole for the model Hamiltonian for the $alpha$-${cal T}_3$ double layer in a magnetic field. The energy dispersion of collective excitations, the spectrum of sound velocity, and the effective magnetic mass of magnetoexcitons are obtained in the integer quantum Hall regime for high magnetic fields. The superfluid density and the temperature of the Kosterlitz-Thouless phase transition are probed as functions of the excitonic density, magnetic field, and the inter-layer separation.
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