In this work, we propose and theoretically investigate a novel side-illuminated graphene Schottky photodetector (SIGS-PD) integrated on an InP waveguide platform suitable for the telecommunication wavelength of 1.55 μm. Bilayer graphene is positioned to absorb the transverse magnetic (TM) mode, with an InP substrate forming a Schottky junction to enable electrical connectivity and carrier separation. Through electrostatic gating, the graphene Fermi level is actively tuned to reach an epsilon-near-zero condition of 0.51 eV, transitioning the optical properties from dielectric to metallic. This supports reconfigurable plasmonic modes confined within the subwavelength graphene layer, interacting strongly with the TM optical mode. Responsivity of TM mode is enhanced 10× TE mode reaching 1.24 A/W at the epsilon-near-zero point for the wavelength of 1.55 μm due to discontinuity and localization of the perpendicular electric field. The maximum responsivity is achieved at reverse bias of 4.5 V for device lengths under 4 μm. Dark current is suppressed to 10-15 A by the rectifying Schottky junction. An internal specific detectivity of 9.6×1012 Jones is predicted along with >25 GHz bandwidth, exploiting combined benefits of plasmonic enhancement and electrical transport control in the hybrid graphene-InP platform. The voltage-tunability of the graphene optical properties provides a pathway to dynamically optimize device performance. This work demonstrates a route towards high-responsivity and high-speed graphene photodetectors seamlessly integrated with photonic integrated circuits.