Abstract Let R be a prime ring with involution ⋆ {\star} , and let σ, τ be endomorphisms on R. For any x , y ∈ R {x,y\in R} , let ( x , y ) σ , τ = x ⁢ σ ⁢ ( y ) + τ ⁢ ( y ) ⁢ x {(x,y)_{\sigma,\tau}=x\sigma(y)+\tau(y)x} and C σ , τ ⁢ ( R ) = { x ∈ R ∣ x ⁢ σ ⁢ ( y ) = τ ⁢ ( y ) ⁢ x } {C_{\sigma,\tau}(R)=\{x\in R\mid x\sigma(y)=\tau(y)x\}} . An additive subgroup U of R is said to be a ( σ , τ ) {(\sigma,\tau)} -right Jordan ideal (resp. ( σ , τ ) {(\sigma,\tau)} -left Jordan ideal) of R if ( U , R ) σ , τ ⊆ U {(U,R)_{\sigma,\tau}\subseteq U} (resp. ( R , U ) σ , τ ⊆ U {(R,U)_{\sigma,\tau}\subseteq U} ), and U is called a ( σ , τ ) {(\sigma,\tau)} -Jordan ideal if U is both a ( σ , τ ) {(\sigma,\tau)} -right Jordan ideal and a ( σ , τ ) {(\sigma,\tau)} -left Jordan ideal of R. A ( σ , τ ) {(\sigma,\tau)} -Jordan ideal U of R is said to be a ( σ , τ ) {(\sigma,\tau)} - ⋆ {\star} -Jordan ideal if U ⋆ = U {U^{\star}=U} . In the present paper, it is shown that if U is commutative, then R is commutative. The commutativity of R is also obtained if ( U , U ) σ , τ ⊆ C σ , τ ⁢ ( R ) {(U,U)_{\sigma,\tau}\subseteq C_{\sigma,\tau}(R)} . Some more results are obtained on the ⋆ {\star} -prime ring with a characteristic different from 2.