  In correlated electronic systems, strong interactions and the interplay
between different degrees of freedom may give rise to anomalous charge
transport properties, which can be tuned by external parameters like
temperature and magnetic field. Recently, magnetic quantum oscillations and
metallic low-temperature thermal conductivity have been observed in the Kondo
insulator YbB$_{12}$, whose resistivity is a few orders of magnitude higher
than those of conventional metals. As yet, these unusual observations are not
fully understood. Here we present a detailed investigation of the behavior of
YbB$_{12}$ under intense magnetic fields using both transport and torque
magnetometry measurements. A low-field Hall anomaly, reminiscent of the Hall
response associated with "strange-metal" physics, develops at $T < 1.5$ K. At
two characteristic magnetic fields ($\mu_0H_1= 19.6$ T and $\mu_0H_2 \sim 31$
T), signatures appear in the Hall coefficient, magnetic torque, and
magnetoresistance. We suggest that they are likely to be field-induced Lifshitz
transitions. Moreover, above 35 T, the background resistivity displays an
unusual, nonmetallic $T^{\alpha}$-behavior, with $\alpha$ being field-dependent
and varying between -1.5 and -2. By normalizing the Shubnikov-de Haas
oscillation amplitude to this $T^{\alpha}$-dependence, the calculated cyclotron
mass becomes more consistent with that deduced from de Haas-van Alphen
oscillations. Our results support a novel two-fluid scenario in YbB$_{12}$: a
Fermi-liquid-like fluid of charge-neutral quasiparticles coexists with charge
carriers that remain in a nonmetallic state. The former experience successive
Lifshitz transitions and develop Landau quantization in applied magnetic
fields, whilst scattering between both fluids allows the Shubnikov-de Haas
effect to be observed in the electrical transport.
