Plasmonic optical nanoantennas offer compelling solutions for enhancing light-matter interactions at the nanoscale. However, until now, their focus has been mainly limited to the visible and near-infrared regions, overlooking the immense potential of the ultraviolet (UV) range, where molecules exhibit their strongest absorption. Here, we present the realization of UV resonant nanogap antennas constructed from paired rhodium nanocubes. Rhodium emerges as a robust alternative to aluminum, offering enhanced stability in wet environments and ensuring reliable performance in the UV range. Our results showcase the nanoantenna's ability to enhance the UV autofluorescence of label-free streptavidin and hemoglobin proteins. We achieve significant enhancements of the autofluorescence brightness per protein by up to 120-fold and reach zeptoliter detection volumes, enabling UV autofluorescence correlation spectroscopy (UV-FCS) at high concentrations of several tens of micromolar. We investigate the modulation of fluorescence photokinetic rates and report excellent agreement between the experimental results and numerical simulations. This work expands the applicability of plasmonic nanoantennas to the deep UV range, unlocking the investigation of label-free proteins at physiological concentrations.