We have reported the experimental observation size effects and surface state on semiconductor Bi_1-xSb_x wires with different diameters and alloy composition. The studied glass-insulated single-crystal wires of Bi_1-xSb_x semiconductor alloys were prepared by liquid-phase casting in accordance with the Ulitovsky method. The wires of all the studied compositions and diameters had the same orientation as that in the pure bismuth wires (1011 along the wire axis). A comprehensive study of the temperature dependences of resistance at T = 1.5-300 K, longitudinal and transverse magnetoresistance and their angular dependences, and SdH oscillations in magnetic fields up to 14 T as a function of wire diameter has been conducted. It has been found that the manifestation of the quantum size effect in TI wires based on semiconductor Bi_1-xSb_x alloys near the gapless state leads to an increase in the energy gap by a factor of 4 at wire diameters of 180 nm, and the SdH oscillation periods at H//C₁, C₂, and C₃ quantitatively differ from values for bulk samples of the respective composition. The longitudinal magnetoresistance (Н//I) has a maximum that linearly depends on wire diameter d, H_max = p_F c/ed. In the Bi-8at%Sb and Bi-17at%Sb, the Fermi momentum component p_F perpendicular to the magnetic induction vector H exceeds the values for pure Bi by a factor of 2 and 5, respectively. The results are discussed in terms of the manifestation of the quantum size effect and the specific features of TIs in low-dimensional structures that require new approaches and applications.