  In contrast to the seminal weak localization prediction of a non-critical
Hall constant ($R_{H}$) at the Anderson metal-insulator transition (MIT),
$R_{H}$ 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 $\gamma$-function, finding that
$\gamma(g_{xy})\simeq$ log$(g_{xy})$ 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 $R_{H}$ at the MIT. We find that these surprising results are
in comprehensive and very good accord with signatures of a novel kind of
localization in disordered NbN near the MIT, providing substantial support for
our "strong" localization view.
