Experimental access to massless Weyl fermions through topological materials promises substantial technological ramifications. Here, we report magneto-transport properties of Bi1−x Sb x alloy near the quantum critical point x = 3% and 3.5%. The two compositions that are synthesized and studied are single crystals of Bi0.97Sb0.03 and Bi0.965Sb0.035. We observe a transition from semimetal to semiconductor with the application of magnetic field in both specimens. An extremely large transverse magnetoresistance (MR) 1.8 × 105% and 8.2 × 104% at 2.5 K and 6 T is observed in Bi0.97Sb0.03 and Bi0.965Sb0.035, respectively. Kohler scaling of transverse MR reveals the crossover from low field quadratic MR to a high field linear MR at low temperatures in both samples. A decrease in longitudinal MR is observed only in Bi0.97Sb0.03 that implies the presence of chiral anomaly associated with the Weyl state at the crossover point (x = 0.03) in Bi1−x Sb x system. The chiral anomaly is absent for the sample Bi0.965Sb0.035. A sharp increase in longitudinal resistivity for Bi0.97Sb0.03 close to zero magnetic fields indicates the weak anti-localization effect in Bi0.97Sb0.03. Extremely high carrier concentrations and high mobilities have been recorded for both the samples.