Identities involving b -generalized skew derivations in prime rings acting as Jordan derivation

Let R symbolize a prime ring with a characteristic other than 2, and let ρ(η1,…,ηn) represent a non-central multilinear polynomial over the extended centroid C of R. Assuming the presence of three b-generalized skew derivations on R, namely D1,D2, and D3 that satisfy the equation D1(ρ)ρ+ρD2(ρ)=D3(ρ2) for all ρ=ρ(η1,…,ηn), where η1,…,ηn are elements of R. In this research paper, our goal is to elucidate all potential configurations of D1,D2, and D3.