  The minimal representation of a semisimple Lie group is a 'small'
infinite-dimensional irreducible unitary representation. It is thought to
correspond to the minimal nilpotent coadjoint orbit in Kirillov's orbit
philosophy. The Segal-Bargmann transform is an intertwining integral
transformation between two different models of the minimal representation for
Hermitian Lie groups of tube type. In this paper we construct a Fock model for
the minimal representation of the orthosymplectic Lie superalgebra
$\mathfrak{osp}(m,2|2n)$. We also construct an integral transform which
intertwines the Schr\"odinger model for the minimal representation of the
orthosymplectic Lie superalgebra $\mathfrak{osp}(m,2|2n)$ with this new Fock
model.
