  Fisher information (I) is investigated for confined hydrogen atom (CHA)-like
systems in conjugate $r$ and $p$ spaces. A comparative study between CHA and
free H atom (with respect to $I$) is pursued. In many aspects, inferences in
CHA are significantly different from free counterpart; that includes its
dependence on $n, l, m$. The role of atomic number and atomic radius is
discussed. Further, a detailed systematic result of $I$ with respect to
variation of confinement radius $r_c$ is presented, with particular emphasis on
\emph{non-zero}-$(l,m)$ states. Several new interesting observations are
recorded. Most of these results are of benchmark quality and presented for the
first time.
