Simple special Jordan superalgebras with associative even part

We describe the simple special unital Jordan superalgebras with associative even part $A$ whose odd part $M$ is an associative module over $A$. We prove that each of these superalgebras, not isomorphic to a superalgebra of nondegenerate bilinear superform, is isomorphically embedded into a twisted Jordan superalgebra of vector type. We exhibit a new example of a simple special Jordan superalgebra. We also describe the superalgebras such that $M\cap[A,M]\ne0$.