  Due to its dominance in the low energy eta-nucleon interaction, the S11
N$^*$(1535) resonance enters as an important ingredient in the analyses of
experiments aimed at finding evidence for the existence of eta-mesic nuclei.
The static properties of the resonance get modified inside the nucleus and its
momentum distribution is used in deciding these properties as well as the
kinematics in the analyses. Here we show that given the possibility for the
existence of an N$^*$-$^3$He quasibound state, the relative momentum
distribution of an N$^*$ and $^3$He inside such a $^4$He is narrower than that
of neutron-$^3$He in $^4$He. Results for the N$^*$-$^{24}$Mg system are also
presented. The present exploratory work could be useful in motivating searches
of exotic N$^*$-nucleus quasibound states as well as in performing analyses of
eta meson production data.
