We present a new method to identify luminous off-nuclear X-ray sources in the outskirts of galaxies from large public redshift surveys, distinguishing them from foreground and background interlopers. Using the 3XMM-DR5 catalog of X-ray sources and the SDSS DR12 spectroscopic sample of galaxies, with the help of this off-nuclear cross-matching technique, we selected 98 sources with inferred X-ray luminosities in the range $10^{41} < L_{rm X} < 10^{44},{rm erg,s}^{-1}$, compatible with hyperluminous X-ray objects (HLX). To validate the method, we verify that it allowed us to recover known HLX candidates such as ESO 243$-$49 HLX$-$1 and M82 X$-$1. From a statistical study, we conservatively estimate that up to $71 pm 11$ of these sources may be fore- or background sources, statistically leaving at least 16 that are likely to be HLXs, thus providing support for the existence of the HLX population. We identify two good HLX candidates and using other publicly available datasets, in particular the VLA FIRST in radio, UKIDSS in the near-infrared, GALEX in the ultra-violet and CFHT Megacam archive in the optical, we present evidence that these objects are unlikely to be foreground or background X-ray objects of conventional types, e.g. active galactic nuclei, BL Lac objects, Galactic X-ray binaries or nearby stars. However, additional dedicated X-ray and optical observations are needed to confirm their association with the assumed host galaxies and thus secure their HLX classification.
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