  The quantum supergroup ${\rm{U}}_q({\mathfrak {osp}}(1|2n))$ admits a finite
dimensional spinor representation, which does not have a classical limit. We
construct a realisation of this representation on the Fock space of
$q$-fermions. We also generalise the construction to the infinite dimensional
spinor representations of ${\rm{U}}_q({\mathfrak {osp}}(2m+1|2n))$ for $m, n\ge
1$ by using both quantum bosons and fermions. This leads to a new realisation
different from those obtained before by other researchers.
