  In this paper, we study a family of fusion and modular systems realizing
fusion categories Grothendieck equivalent to the representation category for
$so(2p+1)_2$. These categories describe non-abelian anyons dubbed `metaplectic
anyons'. We obtain explicit expressions for all the $F$- and $R$-symbols. Based
on these, we conjecture a classification for their monoidal equivalence classes
from an analysis of their gauge invariants and define a function which gives us
the number of classes.
