In contrast to the seminal weak localization prediction of a non-critical Hall constant (RH ) at the Anderson metal-insulator transition (MIT), RH in quite a few real disordered systems exhibits both, a strong T -dependence and critical scaling near their MIT. Here, we investigate these issues in detail within a non-perturbative "strong localization" regime using cluster-dynamical mean field theory (CDMFT). We uncover (i) clear and unconventional quantum-critical scaling of the GellMann-Law, or γ-function for magneto-transport, finding that γ(gxy) =
d[log(gxy)] d[log(T )]≃ log(gxy) over a wide range spanning the continuous MIT, very similar to that seen for the longitudinal conductivity, (ii) strongly T -dependent and clear quantum critical scaling in both transverse conductivity and RH at the MIT. We show that these surprising results are in comprehensive and very good accord with signatures of a novel Mott-like localization in NbN near the MIT, providing substantial support for our "strong" localization view.