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We report the localization of the X-ray emission from two strongly lensedAGN, CLASS B0712+472 ($z=1.34$) and CLASS B1608+656 ($z=1.394$). We obtainmilliarcsecond X-ray astrometry by developing a novel method that combinesparametric lens modelling with a Bayesian analysis. We spatially locate theX-ray sources in CLASS B0712+472 and CLASS B1608+656 within 11 mas and 9 masfrom the radio source, respectively. For CLASS B0712+472, we find that theX-ray emission is co-spatial with the radio and optical emission. While, inCLASS B1608+656, the X-ray emission is co-spatial with radio, but displacedwith respect to the optical emission at 1$\sigma$ level, which positions thissource as an offset AGN candidate. This high astrometric precision improves onthe limitations of existing X-ray instruments by two orders of magnitude. Thedemonstrated method opens a path to search for offset and binary AGN at $z>1$,and to directly test supermassive black hole formation models in a redshiftrange that has been mostly underconstrained to date.

Milliarcsecond X-ray astrometry to resolve inner regions of AGN at $z>1$ using gravitational lensing