This study investigated the impact of samarium and lanthanum fluorides (SmF3 and LaF3) on the physical and mechanical properties of Tl0.8Hg0.2Ba2Ca2−xRxCu3O9−δ−yFy superconducting phases (specifically the (Tl, Hg)-1223 phase), where R = Sm and La, with 0.00 ≤ x ≤ 0.10. The superconducting samples were synthesized using the solid-state reaction method. X-ray diffraction (XRD) verified the formation of the (Tl, Hg)-1223 phase without altering its tetragonal structure. Scanning electron micrographs (SEM) reveal the improvement of the grain size and inter-grain connectivity as Sm and La contents increased up to x=0.025. The electrical properties of (Tl, Hg)-1223 were studied using I-V and electrical resistivity measurements. Improved superconducting transition temperature (Tc) and transport critical current density (Jc) were observed up to x=0.025, beyond which they decreased substantially. Vickers microhardness (Hv) measurements were performed at room temperature to investigate their mechanical performance with various applied loads (0.49–9.80 N) and times (10–90 s). For both substitutions, the mechanical properties were enhanced up to an optimal value at x=0.025. All samples exhibited normal indentation size effect (ISE) behavior. The proportional sample resistance (PSR) model best explained Hv values among five theoretical models. Dislocation creep was the primary creep mechanism in the samples, according to indentation creep studies.