In this article, we present a free-standing terahertz metasurface based on asymmetric S-shaped complementary resonators under normal incidence in transmission mode configuration. Each unit cell of the metasurface consists of two arms of mirrored S-shaped slots. We investigate the frequency response at different geometrical asymmetry via modifying the dimensions of one arm of the resonator. This configuration enables the excitation of asymmetric quasi-bound states in the continuum resonance and, hence, features very good field confinement that is very important for biosensing applications. Moreover, the performance of this configuration as a biosensor was examined for glucose concentration levels from 54 mg/dL to 342 mg/dL. This range covers hypoglycemia, normal, and hyperglycemia diabetes mellitus conditions. Two sample coating scenarios were considered, namely the top layer when the sample covers the metasurface and the top and bottom layers when the metasurface is sandwiched between the two layers. This strategy enabled very large resonance frequency redshifts of 236.1 and 286.6 GHz that were observed for the two scenarios for a 342 mg/dL concentration level and a layer thickness of 20 μm. Furthermore, for the second scenario and the same thickness, a wavelength sensitivity of 322,749 nm/RIU was found, which represents a factor of 2.3 enhancement compared to previous studies. The suggested terahertz metasurface biosensor in this paper could be used in the future for identifying hypoglycaemia and hyperglycemia conditions.