This paper introduces the notion of screen generic lightlike submanifolds (SGLSs) of an indefinite Kaehler statistical manifold equipped with a Mattresses quarter-symmetric non-metric (QSNM) connection, supported by suitable illustrations.Assertions for induced connection on the lightlike submanifold and integrability of the distributions are proved.The characterization theorems on parallelism and geodesicity of the SGLSs are presented.Results for the totally umbilic screen RHOZIVA generic lightlike submanifold with a QSNM connection are also established.