  A series of corrections to general relativity have recently been applied to
find the relationship between entropy and extremality-bound black holes. This
relationship has been investigated for many black holes, such as charged AdS,
rotating, and massive gravity black holes. We give a minor constant correction
to the action and confirm these universal relations for a charged-rotating-AdS
black hole. We then examine these calculations for the black hole, surrounded
by the quintessence and the cloud of string. In this paper, we evaluate a new
universal relation. It means that we find the relation between the extremal
mass of the black hole and the factor of cloud string and observe that the
corresponding universal relation is well established. We find that the
quintessence terms play a very effective role in calculating the mass-charge
ratio and concept of weak gravity conjecture of black holes. We note here that
the added constant correction is inversely related to the entropy of the black
hole. It leads us to see that the mass-to-charge ratio decreases and fully
confirms the black hole's weak gravity conjecture (WGC).
