The problem of convection induced by radial buoyancy in an electrically conducting fluid contained by a rotating cylindrical annulus (angular frequency, Omega) in the presence of a homogeneous magnetic field (B) in the azimuthal direction is considered. The small gap approximation is used together with rigid cylindrical boundaries. The onset of convection occurs in the form of axial, axisymmetric or oblique rolls. The angle psi between the roll axis and the axis of rotation depends of the ratio between the Chandrasekhar number, Q similar to B-2, and the Coriolis number, tau similar to Omega. Fully three-dimensional numerical simulations as well as Galerkin representations for roll patterns including the subsequent stability analysis are used in the theoretical investigation. At finite amplitudes, secondary transitions to 3D-hexarolls and to spatio-temporal chaos are found. Overlapping regions of pattern stability exist such that the asymptotically realized state may depend on the initial conditions.