We search for a possible relationship between weak gravity conjecture (WGC) and conformal field theory (CFT) in hyperscaling violating and Kerr-Newman-AdS black holes. We deal with the critical points of the black hole systems using the correlation function introduced in CFT and discuss WGC conditions using the imaginary part of the energy obtained from the critical points and their poles. Under the assumptions , , and , we link WGC to hyperscaling violating black holes owing to the existence of values larger and smaller than one. For the second black hole system, we study the conditions of WGC for Kerr-Newman-AdS black holes using rotation and radius parameters. Then, we show that the conditions of WGC are satisfied when the charged particle near the hyperscaling violating and Kerr-Newman black holes is with a ratio .

We study the thermodinamic features of static, spherically-symmetric Schwarzschild black holes adopting different types of Barrow entropy. Specifically, in addition to the standard Barrow entropy, we consider a logarithmic-corrected type of this entropy by taking into account some loop quantum gravity effects. Moreover, we investigate the black hole thermodynamics from the viewpoint of Barrow entropy in presence of non-extensivity effects coming from the Tsallis statistics. Finally, we compare the results obtained for different Barrow-based entropies.