A hexagonal lattice birefringent photonic crystal fiber biosensor based on surface plasmon resonance principle has been offered in this paper. Regarding efficient fabrication aspects, simpler unpolished external sensing style has been selected and implemented for unknown refractive index detection. Numerical analysis of operational variables has been executed using the finite element method (FEM). With silica as the core material, indium tin oxide (ITO) is employed to stage the plasmonic interactions against the analyte. The working window is tuned around telecommunication frequencies. Within this comfortable window, this sensor demonstrates maximum sensitivities of 10000 nm/RIU and 541 $\mathrm{R}\mathrm{I}\mathrm{U}^{-1}$ for dynamic index range 1.33-1.37 in spectral and amplitude interrogations respectively. It has also been addressed that let alone the intrinsic tuning, sensitivity as high as 16900 nm/RIU is achievable in longer wavelength region by sheer thickness modification of ITO.