This research explores the possibility of using non-Gaussian class of beam like Bessel-Gauss beam towards the investigation of a highly-sensitive modal interference-based salinity sensor. Such fiber-optic sensor involves a No-core fiber which is being spliced amid two specialty higher order mode supporting fibers. The main motivation behind our proposed work is that Bessel-Gauss beam has higher amount of energy at the beam’s edge which will create larger overlap between the guided modes with the sensing medium without any complex fabrication process. By harnessing such advantages of Bessel-Gauss beam, the efficient excitation of various high-order linearly polarized modes within the sensor structure has been analyzed with emphasis on the coupled mode theory (CMT). To corroborate this, a detailed optical modeling and simulation study on the proposed sensing scheme was performed in mode solutions software (Lumerical Inc, Canada) to predict the propagation behavior of Bessel-Gauss beam within the waveguide structure. Owing to a large number of high-order mode coupling, the proposed sensor unveils a 3.12 fold superior sensitivity as compared to the conventional Gaussian beam-based sensor, with a commendable sensing resolution of 0.005%. Moreover, a detailed simulation study has been executed to examine the sensor behavior for various No-core fiber radii, and axicon apex angles. As the proposed all-fiber salinity sensor features the advantages of higher sensitivity and better sensing resolution, so it has a great prospect in any physical, biological or chemical sensing needs.