  Motivated by the recently discovered time-reversal symmetry-breaking
superconductivity in epitaxial Bi/Ni bilayer system with transition temperature
$T_c\approx 4.2$K and the observation of zero-bias anomaly in tunneling
measurements, we show that gap-filling states can appear in the fully gapped
$d_{xy}\pm id_{x^2-y^2}$ superconducting states. We consider a model of helical
electron states with d-wave pairing. In particular, we show that both magnetic
and non-magnetic impurities can create states within the superconducting gap.
Alternatively, we also show that the coupling of the electron spins to the
in-plane Zeeman field provided by nickel can also create gap-filling states by
producing Bogoliubov Fermi surfaces. Our findings may explain the origin of
zero-bias anomaly observed in the point-contact tunneling measurements.
