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Thanks to the relative ease of finding and characterizing small planets around M dwarf stars, these objects have become cornerstones in the field of exoplanet studies. The current paucity of planets in long-period orbits around M dwarfs make such objects particularly compelling as they provide clues about the formation and evolution of these systems. In this study, we present the discovery of TOI-2257 b (TIC 198485881), a long-period (35 d) sub-Neptune orbiting an M3 star at 57.8pc. Its transit depth is about 0.4%, large enough to be detected with medium-size, ground-based telescopes. The long transit duration suggests the planet is in a highly eccentric orbit ($e \sim 0.5$), which would make it the most eccentric planet that is known to be transiting an M-dwarf star. We combined TESS and ground-based data obtained with the 1.0-m SAINT-EX, 0.60-m TRAPPIST-North and 1.2-m FLWO telescopes to find a planetary size of 2.2 $R_{\oplus}$ and an orbital period of 35.19 days. In addition, we make use of archival data, high-resolution imaging, and vetting packages to support our planetary interpretation. With its long period and high eccentricity, TOI-2257 b falls in a novel slice of parameter space. Despite the planet's low equilibrium temperature ($\sim$ 256 K), its host star's small size ($R_* = 0.311 \pm{0.015}$) and relative infrared brightness (K$_{mag}$ = 10.7) make it a suitable candidate for atmospheric exploration via transmission spectroscopy.