Among exotic pairing states of interacting fermions, the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, characterized by Cooper pairs condensed at finite momentum, has been a long-sought state that remains unresolved in many classes of systems, including superconductors and ultracold atoms. A fascinating aspect of the FFLO state is the emergence of periodic nodal planes in real space, but its observation is still lacking. Here we investigate the order parameter structure for c-axis fields on a high purity single crystal of FeSe. The heat capacity and magnetic torque provide thermodynamic evidence for a distinct superconducting phase at the low-temperature/high-field corner of the phase diagram. Despite the bulk superconductivity, spectroscopic-imaging scanning tunneling microscopy (SI-STM) performed on the same crystal demonstrates that the superconducting order parameter vanishes at the surface upon entering the high-field phase. These results imply that the planar node induced perpendicular to H is pinned at the surface, providing evidence of the FFLO pairing state with zeroth Landau level.