  First, we prove that indefinite Sasakian manifolds do not admit any screen
conformal $r$-null submanifolds, tangent to the structure vector field. We,
therefore, define a special class of null submanifolds, called; {\it contact
screen conformal} $r$-null submanifold of indefinite Sasakian manifolds.
Several characterization results, on the above class of null submanifolds, are
proved. In particular, we prove that such null submanifolds exist in indefinite
Sasakian space forms of constant holomorphic sectional curvatures of $-3$.
