We present the first results of our ongoing chemical study of carbon stars in the Local Group of galaxies . We used spectra obtained with UVES at the 8.2 m Kueyen-VLT telescope and a new grid of spherical model atmospheres for cool carbon-rich stars which include polyatomic opacities , to perform a full chemical analysis of one carbon star , BMB-B 30 , in the Small Magellanic Cloud ( SMC ) and two , IGI95-C1 and IGI95-C3 , in the Sagittarius Dwarf Spheroidal ( Sgr dSph ) galaxy . Our main goal is to test the dependence on the stellar metallicity of the s-process nucleosynthesis and mixing mechanism occurring in AGB stars . For these three stars , we find important s-element enhancements with respect to the mean metallicity ( [ M/H ] ) , namely [ s/M ] \approx +1.0 , similar to the figure found in galactic AGB stars of similar metallicity . The abundance ratios derived between elements belonging to the first and second s-process abundance peaks , corresponding to nuclei with a magic number of neutrons N = 50 ( 88Sr , 89Y , 90Zr ) and N = 82 ( 138Ba , 139La , 140Ce , 141Pr ) , agree remarkably well with the theoretical predictions of low mass ( M < 3 M _ { \odot } ) metal-poor AGB nucleosynthesis models where the main source of neutrons is the ^ { 13 } C ( \alpha,n ) ^ { 16 } O reaction activated during the long interpulse phase , in a small pocket located within the He-rich intershell . The derived C/O and ^ { 12 } C/ ^ { 13 } C ratios are , however , more difficult to reconcile with theoretical expectations . Possible explanations , like the extrinsic origin of the composition of these carbon stars or the operation of a non-standard mixing process during the AGB phase ( such as the cool bottom process ) , are discussed on the basis of the collected observational constraints .