Let $\mathfrak{S}$ be a prime ring with automorphisms $\alpha ,\beta$. A bi-additive map $\mathfrak{D}$ is called an ( $\alpha ,\beta$) Jordan bi-derivation if $\mathfrak{D}(k^2,s)=\mathfrak{D}(k,s)\alpha (k)+\beta (k)\mathfrak{D}(k,s)$. In this paper, we find conditions under which a symmetric ( $\alpha ,\beta$) Jordan bi-derivation becomes a symmetric ( $\alpha ,\beta$) bi-derivation. We also characterize the symmetric $(\alpha ,\beta )$ Jordan bi-derivations.