A novel Schottky barrier MOSFET with quad gate and with source engineering has been proposed in this work. A high-κ dielectric is used at the source side of the channel, while SiO2 is used at the drain side of the channel. To improve the carrier mobility, a SiGe pocket region is created at the source side of the channel. Physical and electrical characteristics of the proposed device are compared with conventional double gate Schottky barrier MOSFET. It has been observed that the proposed device exhibits better performance, with a higher ION/IOFF ratio and lower subthreshold slope. The high-κ dielectric, along with the SiGe pocket region, improves tunneling probability, while aluminum, along with SiO2 at the drain side, broadens the drain/channel Schottky barrier and reduces the hole tunneling probability, resulting in a reduced OFF-state current. Further, the proposed device is used as a biosensor to detect both the charged and neutral biomolecules. Biosensors are made by creating a nanocavity in the dielectric region near the source end of the channel to capture biomolecules. Biomolecules such as streptavidin, biotin, APTES, cellulose and DNA have unique dielectric constants, which modulates the electrical parameters of the device. Different electrical parameters, viz., the electric field, surface potential and drain current, are analyzed for each biomolecule. It has been observed that drain current increases with the dielectric constant of the biomolecules. Furthermore, the sensitivity and selectivity of the proposed biosensors is better than that of conventional biosensors made using double gate Schottky barrier MOSFETs. Sensitivity is almost twice that of a conventional sensor, while selectivity is six to twelve times higher than a conventional one.