Coumarinyl thiosemicarbazone derivatives (1E)‐1‐(1‐(2‐oxo‐2H‐chromen‐3‐yl)ethylidene)thiosemicarbazide (OCET), (1E)‐1‐(1‐(6‐bromo‐2‐ oxo‐2H‐chromen‐3‐yl)ethylidene)thiosemicarbazide (BOCET) and 1‐(1‐(3‐oxo‐3H‐benzo[f]chromen‐2‐yl)ethylidene)thiosemicarbazide (NOCET) and their Rh(III) complexes were synthesized, the characterization was carried out by elemental analysis, IR, UV–Visible, mass, magnetic measurement and molar conductance techniques. Data interpretation of the Rh(III) complexes indicates that the ligands of coumarinyl thiosemicarbazone derivatives were formed in stoichiometric ratios as 1:2 (metal: ligand). The studied ligands act as a bidentate ligand by using both azomethine nitrogen and thiol sulphur as monoanion center of donation. The theoretical conformational structure analyses were performed using density functional theory for ligands and complexes at B3LYP functional with 6‐31G(++)d,p basis set for ligands and LANL2DZ basis set for complexes. The charge distribution within the ligands and its Rh(III) complexes was calculated using Mulliken population analysis of (MPA) and natural population analysis (NPA). The antibacterial activity of the prepared compounds was tested against some types of Gram positive and negative bacteria. Molecular docking investigation proved that, the ligands and complexes had interesting interactions with active site amino acids of ribosyltransferase (code: 3GEY).