  In this paper we study black hole entropy universality within the Conformal
Weyl gravity paradigm. We do this by first computing the entropy of specific
vacuum and non-vacuum solutions, previously unexplored in Conformal Weyl
gravity via both the N\"other current method and Wald's entropy formula. For
the vacuum case, we explore the near horizon near extremal Kerr metric, which
is also a vacuum solution to Conformal Weyl gravity and not previously studied
in this setting. For the non-vacuum case we couple the conformal Weyl gravity
field equations to a near horizon (linear) $U(1)$ gauge potential and analyze
the respective found solutions. We highlight the non-universality of black hole
entropy between our studied black hole solutions of varying symmetries. However
despite non-universality, the respective black hole entropies are in congruence
with Wald's entropy formula for the specific gravity theory. Finally and
despite non-universality, we comment on the construction of a near horizon CFT
dual to one of our unique non-vacuum solutions. Due to the non-universality, we
must introduce a parameter (similarly to entropy calculations in LQG) which we
also call $\gamma$ and relating to the Weyl anomaly coefficient. The
construction follows an $AdS_2/CFT_1$ correspondence in the near horizon, which
enables the computation of the full asymptotic symmetry group of the chosen
non-vacuum conformal Weyl black hole and its near horizon quantum CFT dual. We
conclude with a discussion and outlook for future work.
