  The purpose of this paper is to prove the uniqueness of conical
K\"ahler-Einstein metrics, under the condition that the twisted
$Ding$-functional is proper. This is a generalization of the author's previous
work, and we shall first investigate the uniqueness of twisted
K\"ahler-Einstein metrics, and then use these smooth perturbed solutions to
approximate the actual conical one. Finally, it will bring the uniqueness of
the limiting singular metric.
