  An off-shell generalization of the Abbott-Deser-Tekin (ADT) conserved charge
was recently proposed by Kim et al. They achieved this by introducing off-shell
Noether currents and potentials. In this paper, we construct the crucial
off-shell Noether current by the variation of the Bianchi identity for the
expression of motion equation, with the help of the property of Killing vector.
Our Noether current, which contains an additional term that is just one half of
the Lie derivative of a surface term with respect to the Killing vector, takes
a different form in comparison with the one in their work. Then we employ the
generalized formulation to calculate the quasi-local conserved charges for the
most general charged spherically symmetric and the dyonic rotating black holes
with AdS asymptotics in four-dimensional conformal Weyl gravity, as well as the
charged spherically symmetric black holes in arbitrary dimensional
Einstein-Gauss-Bonnet gravity coupled to Maxwell or nonlinear electrodynamics
in AdS spacetime. Our results confirm those through other methods in the
literature.
