The interplay of magnetic and charge fluctuations can lead to quantum phases with exceptional electronic properties. A case in point is magnetically-driven superconductivity^,, where magnetic correlations fundamentally affect the underlying symmetry and generate new physical properties. The superconducting wavefunction in most known magnetic superconductors does not break translational symmetry. However, it has been predicted that modulated triplet p-wave superconductivity occurs in singlet d-wave superconductors with spin-density-wave (SDW) order^,. Here we report evidence for the presence of a spatially inhomogeneous p-wave Cooper pair-density wave in CeCoIn₅. We show that the SDW domains can be switched completely by a tiny change of the magnetic field direction, which is naturally explained by the presence of triplet superconductivity. Further, the Q-phase emerges in a common magneto-superconducting quantum critical point. The Q-phase of CeCoIn₅ thus represents an example where spatially modulated superconductivity is associated with SDW order.