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We present the first attempt at measuring the baryonic acoustic oscillations (BAOs) in the large-scale cross-correlation between the magnesium-II doublet (Mg ii) flux transmission field and the position of quasar and galaxy tracers. The Mg ii flux transmission continuous field at 0.3 < z < 1.6 is measured from 500,589 quasar spectra obtained in the Baryonic Oscillation Spectroscopic Survey (BOSS) and the extended BOSS (eBOSS). The positions of 246,697 quasar tracers and 1346,776 galaxy tracers are extracted from the Sloan Digital Sky Survey I and II, BOSS, and eBOSS catalogs. In addition to measuring the cosmological BAO scale and the biased matter density correlation, this study allows tests and improvements to cosmological Lyα analyses. A feature consistent with that of the BAOs is detected at a significance of Δχ2 = 7.25. The measured Mg ii linear transmission bias parameters are bMg ii(2796) (z = 0.59) = (−6.82 ± 0.54) × 10−4 and bMg ii(2804) (z = 0.59) = (−5.55 ± 0.46) ×10−4, and the Mg i bias is bMg i(2853) (z = 0.59) = (−1.48 ± 0.24) × 10−4. Their redshift evolution is characterized by the power-law index: γMg = 3.36 ± 0.46. These measurements open a new window toward using BAOs from flux transmission at z < 1 in the final eBOSS sample and in the upcoming sample from the Dark Energy Spectroscopic Instrument. [ABSTRACT FROM AUTHOR]