  Let R be a prime ring of characteristic not equal to 2, U be its Utumi
quotient ring and C be the extended centroid of R. Let \phi be a multilinear
polynomial over C, which is not central valued on R and F, G be two
b-generalized skew derivations on R. The purpose of this article is to describe
all possible forms of the b-generalized skew derivations F and G satisfying the
identity $F (u)u + uG(u) = G(u ^2)$, for all u \in {{\phi}({\zeta}) | {\zeta} =
({\zeta}1 . . . , {\zeta}n) \inR^n}. Consequently, we discuss the cases when
this identity acts as Jordan derivation and 2- Jordan multiplier on prime rings
