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We present the first detailed chemical analysis from APOGEE-2S observations of stars in six regions of recently discovered substructures in the outskirts of the Magellanic Clouds extending to 20° from the Large Magellanic Cloud (LMC) center. We also present, for the first time, the metallicity andα-abundance radial gradients of the LMC and the Small Magellanic Cloud (SMC) out to 11° and 6°, respectively. Our chemical tagging includes 13 species including light,α-, and Fe-peak elements. We find that the abundances of all of these chemical elements in stars populating two regions in the northern periphery, along the northern “stream-like” feature, show good agreement with the chemical patterns of the LMC, and thus likely have an LMC origin. For substructures located in the southern periphery of the LMC we find more complex chemical and kinematical signatures, indicative of a mix of LMC-like and SMC-like populations. The southern region closest to the LMC shows better agreement with the LMC, whereas that closest to the SMC shows a much better agreement with the SMC chemical pattern. When combining this information with 3D kinematical information for these stars, we conclude that the southern region closest to the LMC likely has an LMC origin, whereas that closest to the SMC has an SMC origin and the other two southern regions have a mix of LMC and SMC origins. Our results add to the evidence that the southern substructures of the LMC periphery are the product of close interactions between the LMC and SMC, and thus likely hold important clues that can constrain models of their detailed dynamical histories.