We report our results from a set of high-resolution, two-fluid, non-linear simulations of the magnetized Rayleigh Taylor instability (RTI) at the interface between a solar prominence and the corona. These data follow results reported earlier on linear and early non-linear RTI dynamics in this environment. This paper is focused on the generation and amplification of magnetic structures by RTI. The simulations use a two-fluid model that includes collisions between neutrals and charges, including ionization and recombination, energy and momentum transfer, and frictional heating. The 2.5D magnetized RTI simulations demonstrate that in a fully developed state of RTI, a large fraction of the gravitational energy of a prominence thread can be converted into quasi-turbulent energy of the magnetic field. The RTI magnetic energy generation is further accompanied by magnetic and plasma density structure formation, including dynamic formation, break-up, and merging of current sheets and plasmoid sub-structures. The flow decoupling between neutrals and charges, as well as ionization and recombination reactions, are shown to have significant impact on the structure formation in a magnetized RTI.