The physics of the solar dark matter (DM) that are captured and thermalise through the DM-nucleon interaction has been extensively studied. In this work, we consider the leptophilic DM scenario where the DM particles interact exclusively with the electrons through the axial-vector coupling... We investigate relevant phenomenologies in the Sun, including its capture, evaporation and thermalisation, and we calculate the equilibrium distribution using the Monte Carlo methods, rather than adopting a semi-analytic approximation. Based on the analysis, we then determine the minimum testable mass for which the DM-electron coupling strength can be probed via the neutrino observation. Compared to the case of the DM-nucleon interaction, it turns out that minimum detectable mass of the DM-electron interaction is roughly 1 GeV smaller, and a cross section about two orders of magnitude larger is required for the saturation of the annihilation signal. (read more)