String Theory suggests existence of primordial Kerr superspinars, extremely compact objects with external spacetime described by the Kerr naked singularity geometry. The primordial Kerr superspinars have to be converted to a near-extreme black hole due to accretion, but they could survive to the era of highly redshifted quasars. We study the shape of the profiled spectral lines generated by radiating rings or the innermost parts of Keplerian discs orbiting the Kerr superspinars. Influence of the superspinar surface location on the profiled lines is also considered. We demonstrate strong difference of the character of the profiled lines generated by radiating rings for all values of the superspinar spin and all values of the inclination angles of the observer when compared to those generated in the field of Kerr black holes. For small and mediate inclination angles there are large quantitative differences in the extension and position of the lines. For large inclination angles even stro