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Topological insulators possess a non-conductive bulk and present surface states, henceforth, they are electrically conductive along their boundaries. Bismuth selenide ($Bi_2Se_3$) is one of the most promising topological insulators. However, a major drawback is its n-type nature arising from its natural doping, which makes the transport in the bulk dominant. This effect can be overcome by shifting the chemical potential into the bandgap, turning the transport of the surface states to be more pronounced than the bulk counterpart. In this work, $Bi_2Se_3$ was grown by molecular beam epitaxy and doped with 0.8, 2, 7, and 14 at. % of Ga, with the aim of shifting the chemical potential into the bandgap. The structural, morphological, and electronic properties of the Ga doped $Bi_2Se_3$ are studied. Raman and X-ray diffraction measurements confirmed the incorporation of the dopants into the crystal structure. Transport and magnetoresistance measurements in the temperature range of 1.5 to 300 K show that Ga-doped $Bi_2Se_3$ is n-type with a bulk charge carrier concentration of $10^{19} cm^{-3}$. Remarkably, magnetotransport of the weak antilocalization effect (WAL) measurements confirm the existence of surface states up to a doping percentage of 2 at. % of Ga and coherence length values between 50-800 nm, which envisages the possibility of topological superconductivity in this material.