Recent efforts to detect and manipulate Majorana fermions in solid state devices have employed topological insulator (TI) nanowires proximity coupled to superconducting (SC) leads. This combination holds some promises for the fundamental physics and applications. We studied the transverse magnetoresistance (MR) of polycrystal Bi₂Te₂Se and single-crystal Bi_0.83Sb_0.17 TI microwires contacted with superconducting In₂Bi leads. Bi₂Te₂Se has a simple band structure with a single Dirac cone on the surface and a large non-trivial bulk gap of 300 meV. The semiconducting alloy Bi_0.83Sb_0.17 is a strong topological insulator due to the inversion symmetry of bulk crystalline Bi and Sb. To study the TI/SC interface, we prepared Bi₂Te₂Se and Bi_0.83Sb_0.17 glass-coated microwire samples using superconducting alloy In₂Bi (T_c = 5.6 K) to provide a contact of one side of the microwires with copper leads and gallium to provide a contact of the other side of microwires with copper leads. The MR oscillations equidistant in a transverse magnetic field (up to 1 T) at the TI/SC interface were observed at various temperatures (4.2 K–1.5 K) in both the Bi₂Te₂Se and Bi_0.83Sb_0.17 samples. In the Bi₂Te₃ sample with a diameter of d = 17 µm, this oscillations exist with a period of ΔB = 18 mT; in the Bi_0.83Sb_0.17 sample with d = 1.7 µm MR oscillations are characterized by a period of ΔB = 46 mT. The observed oscillations cannot be referred to the Shubnikov de Haas oscillations because they are not periodic in an inverse magnetic field and their amplitude decreases with increasing magnetic field. Most probably, transverse MR oscillations arise owing to the appearance of highly conducting edge states on the planar boundary of SC/TI.