The superconductor-insulator transition in a transverse magnetic field is studied in a highly disordered MoC film with the product of the Fermi momentum and the mean free path k F l close to unity. Surprisingly, the Zeeman paramagnetic effects dominate over orbital coupling on both sides of the transition. In the superconducting state it is evidenced by a high upper critical magnetic field B c 2 , by its square-root dependence on temperature, as well as by the Zeeman splitting of the quasiparticle density of states (DOS) measured by scanning tunneling microscopy. At B c 2 a logarithmic anomaly in DOS is observed. This anomaly is further enhanced in an increasing magnetic field, which is explained by the Zeeman splitting of the Altshuler-Aronov DOS driving the system into a more insulating or resistive state. A spin-dependent Altshuler-Aronov correction is also needed to explain the transport behavior above B c 2 .