  Magnetic topological insulators (MnBi$_2$Te$_4$)(Bi$_2$Te$_3$)$_n$ were
anticipated to exhibit magnetic energy gaps while recent spectroscopic studies
did not observe them. Thus, magnetism on the surface is under debate. In this
work, we propose another symmetry criterion to probe the surface magnetism.
Because of both time-reversal symmetry-breaking and inversion
symmetry-breaking, we demonstrate that the surface band structure violates
momentum-inversion symmetry and leads to a three-fold rather than six-fold
rotational symmetry on the Fermi surface if corresponding surface states couple
strongly to the surface magnetism. Such a momentum-inversion symmetry violation
is significant along the $\Gamma-K$ direction for surface bands on the (0001)
plane.
