  Coupled laboratory-numerical experiments of Rayleigh-B\'enard convection
(RBC) in liquid gallium subject to a vertical magnetic field are presented. The
experiments are carried out in two cylindrical containers with
diameter-to-height aspect ratio $\Gamma = 1.0$ and $2.0$ at varying thermal
forcing (Rayleigh numbers $10^5 \lesssim Ra \lesssim 10^8$) and magnetic field
strength (Chandrasekhar numbers $0\lesssim Ch \lesssim 3\times 10^5$).
Laboratory measurements and numerical simulations confirm that
magnetoconvection in our finite cylindrical tanks onsets via non-drifting
wall-attached modes, in good agreement with asymptotic predictions for a
semi-infinite domain. With increasing supercriticality, the experimental and
numerical thermal measurements and the numerical velocity data reveal
transitions between wall mode states with different azimuthal mode numbers and
between wall-dominated convection to wall and interior multimodality. These
transitions are also reflected in the heat transfer data, which combined with
previous studies, connect onset to supercritical turbulent behaviors in liquid
metal magnetoconvection over a large parameter space. The gross heat transfer
behaviors between magnetoconvection and rotating convection in liquid metals
are compared and discussed.
