Supermassive black holes (SMBHs) power active galactic nuclei (AGN). The vicinity of the SMBH has long been proposed as the potential site of particle acceleration and neutrino production. Recently, IceCube reported evidence of neutrino emission from the Seyfert II galaxy NGC 1068. The absence of a matching flux of TeV gamma rays suggests that neutrinos are produced where gamma rays can efficiently get attenuated, for example, in the hot coronal environment near the SMBH at the core of the AGN. Here, we select the intrinsically brightest (in X-ray) Seyfert galaxies in the Southern Sky from the BAT AGN Spectroscopic Survey (BASS) and search for associated neutrinos using starting track events in IceCube. In addition to the standard power law flux assumption, we leverage a dedicated disc-corona model of neutrino production in such an environment in order to improve the discovery potential of the search. In this contribution, we report on the expected performance of our searches for neutrinos from these Seyfert galaxies.