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In this paper, we consider the singular photonic spin Hall effect (PSHE) in a chiral-graphene-chiral (CGC) heterostructure in the THz band. We investigate the impact of a chiral medium on reflectance spectra and the modulation of the Fermi energy on the surface conductivity of graphene. Our study shows that placing a chiral medium on both sides of a monolayer of graphene results in an enhanced transverse shift (TS) compared to placing a non-chiral medium. Moreover, the direction of the TS of the PSHE can be altered by adjusting the sign of the chirality parameter and the Fermi energy of graphene. Finally, we establish a quantitative relationship between the PSHE and the chirality parameter and the Fermi energy of graphene. By dynamically modulating the PSHE in graphene, it is possible to flexibly detect chirality parameters. This work opens up new avenues for chiral molecular detection and graphene-PSHE dynamic modulation.