  The unimodularity condition for a Poisson structure (ie., a Poisson structure
with a trivial modular class) induces a Poincar\'e duality between its Poisson
homology and its Poisson cohomology. Therefore an information about the Poisson
homology of this kind Poisson structures induces by duality an information
about its Poisson cohomology and vise versa. But this is not longer true in the
case of a non trivial modular class. That is the case of Generalized Jacobian
Poisson Structures (GJPS). In this paper, we consider certain GJPS in dimension
3 and obtain properties of their Poisson homological groups and their Poisson
cohomological groups. More precisely, under some assumptions, we obtain the
Poincar\'e series of these Poisson homological groups and we compute explicitly
these Poisson cohomological groups, except the second group which seems more
complicated to obtain.
