We describe FESOM-C, the coastal branch of the Finite-volumE Sea ice -- Ocean Model (FESOM2), which shares with FESOM2 many numerical aspects, in particular, its finite-volume cell-vertex discretization. Its dynamical core differs by the implementation of time stepping, the use of terrain-following vertical coordinate and formulation for hybrid meshes composed of triangles and quads. The first two distinctions were critical for coding FESOM-C as an independent branch. The hybrid mesh capability improves numerical efficiency, since quadrilateral cells have fewer edges than triangular cells. They do not suffer from spurious inertial modes of the triangular cell-vertex discretization and need less dissipation. The hybrid mesh capability allows one to use quasi-quadrilateral unstructured meshes, with triangular cells included only to join quadrilateral patches of differt resolution or instead of strongly deformed quadrilateral cells. The description of the model numerical part is complemented by test cases illustrating the model performance.