  This paper investigates a hypothesis proposed in previous research relating
neutron star (NS) mass and its dark matter (DM) accumulation. As DM
accumulates, NS mass decreases, predicting lower NS masses toward the Galactic
center. Due to limited NSs data near the galactic center, we examine NSs
located within DM clumps. Using the CLUMPY code simulations, we determine the
DM clumps distribution, with masses from 10 to $10^{8}$ $M_{\odot}$ and scales
from $10^{-3}$ to 10 kpc. These clumps' DM exhibit a peak at the center,
tapering toward the outskirts, resembling our Galaxy's DM distribution.
  We analyse these DM clumps' NS mass variations, considering diverse DM
particle masses and galaxy types. We find relatively stable NS mass within 0.01
to 5 kpc from the clump center. This stability supports the initial hypothesis,
particularly for NSs located beyond 0.01 kpc from the clump center, where NS
mass reaches a plateau around 0.1 kpc. Nevertheless, NS mass near the clump's
periphery reveals spatial dependence: NS position within DM clumps influences
its mass in Milky Way-type galaxies. Moreover, this dependence varies with the
DM model considered.
  In summary, our study investigates the proposed link between NS mass and DM
accumulation by examining NSs within DM clumps. While NS mass remains stable at
certain distances from the clump center, spatial dependencies arise near the
clump's outer regions, contingent on the specific DM model.

Astrophysics of Galaxies;Cosmology and Nongalactic Astrophysics;High Energy Astrophysical Phenomena;High Energy Physics - Phenomenology