  In this paper, we consider the Yang-Mills-Higgs flow for twisted Higgs pairs
over K\"ahler manifolds. We prove that this flow converges to a reflexive
twisted Higgs sheaf outside a closed subset of codimension $4$, and the
limiting twisted Higgs sheaf is isomorphic to the double dual of the graded
twisted Higgs sheaves associated to the Harder-Narasimhan--eshadri filtration
of the initial twisted Higgs bundle.
