We examine the properties of topological strongly correlated superconductor
with bond disorder on triangular lattice and demonstrate that our theoretical
(t-J-U) model exhibits some unique features of the Cu-doped apatite
Pb10−xCux(PO4)6O. Namely, the paired state
appears only for carrier concentration 0.8≲x<1 and is followed by
a close-by phase separation into the superconducting and Mott insulating parts.
Furthermore, a moderate amount of the bond disorder (Δt/t≲20%) does not alter essentially the topology with robust Chern number C=2
which diminishes beyond that limit. A room-temperature superconductivity is
attainable only for the exchange to hopping ratio J/∣t∣≥1 if one takes
the bare bandwidth suggested by current DFT calculations. The admixture of
s-wave pairing component is induced by the disorder. The results have been
obtained within statistically consistent variational approximation (SGA)