TOI-4559 is a cool M-dwarf (about 0.39 solar masses, 3,558 K, 0.37 solar radii), 31.6 light-years from Earth. TOI-4559 b is a planet with 1.4 Earth radii, with an orbital period of 4.0 days, at 0.036 AU from its star, and an equilibrium temperature near 554 K, discovered in 2024 via transit. The planet was found when it crossed the face of its star, producing periodic dips in brightness that reveal its size and orbital period to space-based photometry. TOI-4559 b skims its star closer than Mercury orbits the Sun.