  Pairing symmetry plays a central role in the study of superconductivity. It
is usually characterized by integer partial-waves, for example, $s$-, $p$-,
$d$-waves. In this article, we investigate a new class of topological
superconductivity whose gap functions possess a half-odd-integer monopole
charge and, therefore, fractionalized half-odd-integer partial-wave symmetry in
three dimensions. This exotic pairing occurs between Fermi surfaces of which
Chern numbers are differed by an odd integer. The corresponding superconducting
gap function is represented by monopole harmonics with half-odd-integer
monopole charges, and thus carries spinor partial-wave symmetries. The spinor
gap function can exhibit an odd number of nodes on a closed Fermi surface,
which distinguishes it from all the previously known superconducting pairing
symmetry. In the presence of spatial inhomogeneity of order parameters, its
superfluid velocity exhibits a fractionalized Mermin-Ho relation.
