  Motivated by the recent observation of the shell effect in a nanoscale pure
superconductor by Bose {\em et al} [Nat. Mat. {\bf 9}, 550 (2010)], we explore
the possible shell-like effect in a strongly disordered superconductor as it is
known to produce nanosize superconducting puddles (SPs). We find a remarkable
change in the texture of the pairing amplitudes that is responsible for forming
the SP, upon monotonic tuning of the average electron density, $\langle n
\rangle$, and keeping the disorder landscape unaltered. Both the spatially
averaged pairing amplitude and the quasiparticle excitation gap oscillate with
$\langle n \rangle$. This oscillation is due to a rapid change in the low-lying
quasiparticle energy spectra and thereby a change in the shapes and positions
of the SPs. We establish a correlation between the formation of SPs and the
shell-like effect. The experimental consequences of our theory are also
discussed.
