  In this paper we study gradient Ricci-Harmonic soliton with structure of
warped product manifold. We obtain some triviality results for the potential
function, warping function and the harmonic map which reaches maximum or
minimum. In order to obtain nontrivial examples of warped product gradient
Ricci-harmonic soliton, we consider the base and fiber conformal to a
semi-Euclidean space which is invariant under the action of a translation group
of co-dimension one. This approach provide infinitely many geodesically
complete examples in the semi-Riemannian context, which is not contemplated in
the Riemannian case by the Theorem 1.2 in [17].
