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We introduce a class of Lie conformal superalgebra  S ( a ,  b ), where  a ,  b  are complex parameters. These Lie conformal superalgebras can be viewed as the super deformation of Heisenberg-Virasoro type Lie conformal algebras. We classify the free conformal modules of rankover  S ( a ,  b ) for all. Using a Cheng-Kac’s lemma, we also classify the finite irreducible conformal modules over  S ( a ,  b ).

Representations of super deformation of Heisenberg-Virasoro type Lie conformal algebras