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The quasar class of extreme Population A (xA) (also known as super-Eddington accreting massive black holes, SEAMBHs) has been hailed as potential distance indicators for cosmology. The aim of this paper is to define tight criteria for their proper identification starting from the main selection criterion $R_{FeII} > 1 $, and to identify potential intruders not meeting the selection criteria, but nonetheless selected as xA because of the coarseness of automatic searches. Inclusion of the spurious xA sources may dramatically increase the dispersion in the Hubble diagram of quasars obtained from virial luminosity estimates. We studied a sample of 32 low-$z$ quasars originally selected from the SDSS DR7 as xA. All of them show moderate-to-strong FeII emission and the wide majority strong absorption features in their spectra are typical of fairly evolved stellar populations. We performed a simultaneous fit of a host galaxy spectrum, AGN continuum, FeII template and emission lines to spectra, using the fitting technique based on ULySS, full spectrum fitting package. For sources in our sample (of spectral types corresponding to relatively low Eddington ratio), we found an overall consistency between narrow components of H$β$ and [OIII]$λλ$4959, 5007 line shifts and the mean stellar velocity obtained from the host galaxy fit (within $\lesssim |60|$ km/s). Only one source in our sample qualify as xA source. We found high fraction of host galaxy spectrum (in half of the sample even higher then 40\%). When absorption lines are prominent, and the fraction of the host galaxy is high, SSP is mimicking FeII, and that may result in a mistaken identification of FeII spectral features. We have identified several stellar absorption lines that, along with the continuum shape, may lead to an overestimate of $R_{FeII}$, and therefore to the misclassification of sources as xA sources.