The main purpose of the present paper is to study the geometry of transversal lightlike submanifolds and radical transversal lightlike submanifolds of metallic semi-Riemannian manifolds. We investigate the geometry of distributions and obtain necessary and sufficient conditions for the induced connection on these manifolds to be a metric connection. We also obtain characterization of transversal lightlike submanifolds of metallic semi-Riemannian manifolds. Finally, we give two examples.