Non-Abelian half-quantum vortices in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mrow /><mml:mn>3</mml:mn></mml:msup><mml:msub><mml:mi>P</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math> topological superfluids

${}^{3}P_{2}$ superfluids realized in neutron stars are the largest topological quantum matters our Universe. We establish existence and stability of non-Abelian half-quantum vortices (HQVs) with strong magnetic fields. Using a self-consistent microscopic approach, we find that singly quantized vortex is energetically destabilized into pair two HQVs owing to strongly spin-orbit-coupled pairing. topologically protected Majorana fermion on each HQV, thereby providing two-fold anyons characterized by both fermions first homotopy group.