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In this paper, we introduce screen slant lightlike submanifold of an indefinite Sasakian manifold and give examples. We prove a characterization theorem for the existence of screen slant lightlike submanifolds. We also obtain integrability conditions of both screen and radical distributions, prove characterization theorems on the existence of minimal screen slant lightlike submanifolds and give an example of proper minimal screen slant lightlike submanifolds of R92.