Sharp Weyl laws with singular potentials

We consider the Laplace--Beltrami operator on a three-dimensional Riemannian manifold perturbed by potential from Kato class and study whether various forms of Weyl's law remain valid under this perturbation. show that pointwise Weyl holds, modified an additional term, for any with standard sharp remainder term. The term is always lower order than leading but it may or not be In particular, we provide examples singular potentials which violates Laplace-Beltrami operator. For proof extend method Avakumovi\'c to case Schr\"odinger operators potentials.