  We consider the structure of Jordan $H$-pseudoalgebras which are linearly
finitely generated over a Hopf algebra $H$. There are two cases under
consideration: $H=U(\mathfrak h)$ and $H=U(\mathfrak h)# \mathbb C[\Gamma ]$,
where $\mathfrak h$ is a finite-dimensional Lie algebra over $\mathbb C$,
$\Gamma $ is an arbitrary group acting on $U(\mathfrak h)$ by automorphisms. We
construct an analogue of the Tits-Kantor-Koecher construction for finite Jordan
pseudoalgebras and describe all simple ones.
