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Aims. We conducted a high-precision differential abundance analysis of the remarkable binary system HD 240429/30 (Krios and Kronos, respectively), whose difference in metallicity is one of the highest detected to date in systems with similar components (~0.20 dex). A condensation temperatureT_Ctrend study was performed to search for possible chemical signatures of planet formation. In addition, other potential scenarios are proposed to explain this disparity. Methods. Fundamental atmospheric parameters (T_eff, logg, [Fe/H],υ_turb) were calculated using the latest version of the FUNDPAR code in conjunction with ATLAS12 model atmospheres and the MOOG code, considering the Sun and then Kronos as references, employing high-resolution MAROON-X spectra. We applied a full line-by-line differential technique to measure the abundances of 26 elements in both stars with equivalent widths and spectral synthesis taking advantage of the non-solar-scaled opacities to achieve the highest precision. Results. We find a difference in metallicity of ~0.230 dex: Kronos is more metal rich than Krios. This result denotes a challenge for the chemical tagging method. The analysis encompassed the examination of the diffusion effect and primordial chemical differences, concluding that the observed chemical discrepancies in the binary system cannot be solely attributed to any of these processes. The results also show a noticeable excess of Li of approximately 0.56 dex in Kronos, and an enhancement of refractories with respect to Krios. A photometric study with TESS data was carried out, without finding any signal of possible transiting planets around the stars. Several potential planet formation scenarios were also explored to account for the observed excess in both metallicity and lithium in Kronos; none was definitively excluded. While planetary engulfment is a plausible explanation, considering the ingestion of an exceptionally high mass, approximately ~27.8M_⊕, no scenario is definitively ruled out. We emphasize the need for further investigations and refinements in modelling; indispensable for a comprehensive understanding of the intricate dynamics within the Krios and Kronos binary system. 

The sub-Jovian desert is a region in the mass-period and radius-period parameter space that typically encompasses short-period ranges between super-Earths and hot Jupiters, and exhibits an intrinsic dearth of planets. This scarcity is likely shaped by photoevaporation caused by the stellar irradiation received by giant planets that have migrated inward. We report the detection and characterization of TOI-3568 b, a transiting super-Neptune with a mass of 26.4 ± 1.0 M_⊕, a radius of 5.30 ± 0.27 R_⊕, a bulk density of 0.98 ± 0.15 g cm⁻³, and an orbital period of 4.417965 (5) d situated in the vicinity of the sub-Jovian desert. This planet orbiting a K dwarf star with solar metallicity was identified photometrically by the Transiting Exoplanet Survey Satellite (TESS). It was characterized as a planet by our high-precision radial-velocity (RV) monitoring program using MAROON-X at Gemini North, supplemented with additional observations from the SPICE large program with SPIRou at CFHT. We performed a Bayesian MCMC joint analysis of the TESS and ground-based photometry, and MAROON-X and SPIRou RVs, to measure the orbit, radius, and mass of the planet, as well as a detailed analysis of the high-resolution flux and polarimetric spectra to determine the physical parameters and elemental abundances of the host star. Our results reveal TOI-3568 b to be a hot super-Neptune rich in hydrogen and helium, with a core of heavier elements of between 10 and 25 M_⊕in mass. We analyzed the photoevaporation status of TOI-3568 b and find that it experiences one of the highest extreme-ultraviolet (EUV) luminosities among planets with a mass of M_p< 2 M_Nep, yet it has an evaporation lifetime exceeding 5 Gyr. Positioned in the transition between two significant populations of exoplanets on the mass-period and energy diagrams, this planet presents an opportunity to test theories concerning the origin of the sub-Jovian desert.