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In the present study, the concept of Sasakian statistical manifold has been generalized to indefinite Sasakian statistical manifolds. We also introduce lightlike hypersurfaces of an indefinite Sasakian statistical manifold and establish relations between induced geometrical objects with respect to dual connections. Finally, invariant lightlike submanifold of indefinite Sasakian statistical manifold is proved to be an indefinite Sasakian statistical manifold.