  In this paper, we present a detailed study on the phase diagrams of
superconducting topological surface states, especially, focusing on the
interplay between crystalline symmetry and topology of the effective BdG
Hamiltonian. We show that for the $4\times 4$ kinematic Hamiltonian of the
normal state, a mirror symmetry $\mathcal{M}$ can be defined, and for the
$\mathcal{M}$-odd pairings, the classification of the $8\times8$ BdG
Hamiltonian is $\mathbb{Z}\oplus\mathbb{Z}$, and the time-reversal symmetry is
broken intrinsically. The topological non-trivial phase can support chiral
Majorana edge modes, and can be realized in the thin films of iron-based
superconductor such as FeSeTe.
