We report the peculiar chemical abundance patterns of eleven atypical Milky Way ( MW ) field red giant stars observed by the Apache Point Observatory Galactic Evolution Experiment ( APOGEE ) . These atypical giants exhibit strong Al and N enhancements accompanied by C and Mg depletions , strikingly similar to those observed in the so-called second-generation ( SG ) stars of globular clusters ( GCs ) . Remarkably , we find low-Mg abundances ( [ Mg/Fe ] < 0.0 ) together with strong Al and N overabundances in the majority ( 5/7 ) of the metal-rich ( [ Fe/H ] \gtrsim - 1.0 ) sample stars , which is at odds with actual observations of SG stars in Galactic CGs of similar metallicities . This chemical pattern is unique and unprecedented among MW stars , posing urgent questions about its origin . These atypical stars could be former SG stars of dissolved GCs formed with intrinsically lower abundances of Mg and enriched Al ( subsequently self-polluted by massive AGB stars ) or the result of exotic binary systems . We speculate that the stars Mg-deficiency as well as the orbital properties suggest that they could have an extragalactic origin . This discovery should guide future dedicated spectroscopic searches of atypical stellar chemical patterns in our Galaxy ; a fundamental step forward to understand the Galactic formation and evolution .