  We study quantized vortices in ${}^{3}P_{2}$ superfluids using a microscopic
theory for the first time. The theory is based on the Eilenberger equation to
determine the order parameters and the Bogoliubov-de Gennes (BdG) equation to
obtain the eigenenergies and the core magnetization. Within axisymmetric vortex
configurations, we find several stable and metastable vortex configurations
which depend on the strength of a magnetic field, similar to a $v$ vortex and
$o$ vortex in $^3$He superfluids. We demonstrate that the $o$ vortex is the
most stable axisymmetric vortex in the presence of a strong magnetic field, and
we find two zero-energy Majorana fermion bound states in the $o$-vortex core.
We show that the profiles of the core magnetization calculated using the BdG
equation are drastically different from those calculated using only the order
parameter profiles known before.
