  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
$\mathrm{Pb_{10-\mathit{x}}Cu_\mathit{x}(PO_4)_{6}O}$. Namely, the paired state
appears only for carrier concentration $0.8 \lesssim n < 1$ per Cu and is
followed by a close-by phase separation into the superconducting and Mott
insulating parts. Furthermore, a moderate amount of the bond disorder ($\Delta
t / t \lesssim 20 \%$) 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 $J/|t|
\ge 1$ 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).
