  In this paper zero modes of fluctuation are dissected around the two species
of BPS vortices existing in the critical Higgs phase, where the scalar and
vector meson masses are equal, of a gauged $\mathbb{U}(1)$ nonlinear
$\mathbb{CP}^1$-model. If $2\pi n$, $n\in \mathbb{Z}$, is the quantized
magnetic flux of the two species of BPS vortex solutions, $2n$ linearly
independent vortex zero modes for each species are found and described. The
existence of two species of moduli spaces of dimension $2n$ of these stringy
topological defects is thus locally shown.
