  Critical parameters in three screened potentials, namely, Hulth\'en, Yukawa
and exponential cosine screened Coulomb potential are reported. Accurate
estimates of these parameters are given for each of these potentials, for all
states having $n \leq 10$. Comparison with literature results is made, wherever
possible. Present values compare excellently with reference values; for higher
$n,\ell$, our results are slightly better. Some of these are presented for
first time. Further, we investigate the spherical confinement of H atom
embedded in a dense plasma modeled by an exponential cosine screened potential.
Accurate energies along with their variation with respect to box size and
screening parameter are calculated and compared with reference results in
literature. Sample dipole polarizabilities are also provided in this case. The
generalized pseudospectral method is used for accurate determination of
eigenvalues and eigenfunctions for all calculations.
