  We study the sodium-iridates model on the honeycomb lattice with both BCS
pairing potential and Hubbard interaction term. It is shown that this model can
be exactly solved with appropriate choices of amplitude of pairing gaps, where
the interacting terms are transformed to external field terms. The band
structures of these exact solutions on both torus and cylinder geometry are
discussed in great details. It is found that the ground state assumes an
anti-ferromagnetic configuration, which breaks the time reversal symmetry
spontaneously and renders the superconductor topologically trivial. On the
other hand, the nontrivial topology is preserved with ferromagnetic
configuration and can be characterized by the isospin Chern number.
