Over the [Formula: see text]-dimensional supercircle [Formula: see text], we consider the action of the orthosymplectic Lie superalgebra [Formula: see text], by the Lie derivative on the superpseudodifferential operators [Formula: see text]. We compute the [Formula: see text]-relative cohomology spaces [Formula: see text], where [Formula: see text] is the affine Lie superalgebra on [Formula: see text]. We explicitly give cocycles spanning these cohomology spaces. We study the [Formula: see text]-trivial deformations of the structure of the [Formula: see text]-modules [Formula: see text].