  Recent experiments reported the puzzling zero energy modes associated with
ferromagnetic impurities in some iron-based superconductors with topological
band structures. Here, we show that the sufficiently strong exchange coupling
between a ferromagnetic impurity and substrate can trigger a quantum phase
transition, beyond which, the phase of the topological surface superconducting
order parameter around the impurity acquires a sign-change. In such a case, we
prove that a Kramers degenerate pair of Majorana modes can be induced at the
boundary separating the two sign-change regimes and trapped around the impurity
in the topological surface superconducting state. Furthermore, we show that our
theory can explain the controversial observations and confusing features of the
zero energy modes from recent experiments in some iron-based superconductors.
