In this manuscript, split gate dielectric modulated gate-all-around junctionless metal oxide field-effect transistor (SG-GAA-JLFET) based on III-V compound (InGaAs) has recently come forward as a potentiated device in biosensors design due to ultra-sensitivity, selectivity & real-time label-free detection capabilities. In this paper, the boundary conditions at the edges of the junctions are discussed, and their consequences on the Analytical modeling in GAA-JLFET are investigated. The channel-center potential equation is computed by evaluating 2-D Poisson's equation based on the parabolic-potential technique. Additionally, the change of device dimensional parameters upon biosensor sensitivity is computed to investigate the dielectric modulation effects for neutral and charge biomolecules, per se. A SILVACO TCAD simulation tool is utilized for verification and validation of the proposed analytical model. The sensitivity metric of the neutral analyte with a higher dielectric constant is found raised. The value of surface potential sensitivity for Gelatin (k = 12) is seen as 72 which is proportionately 31%, 60%, and 200% greater compared to the sensitivity of apomyoglobin (k = 8), Bacteriophage T7 (k = 6.3), as well as Glucose Oxidase (k = 3.46) for cavity length equal to 20 nm.