  The gas surrounding first-generation (Pop III) stars is expected to emit a
distinct signature in the form of the HeII recombination line at 1640~\AA
(HeII$\lambda$1640). Here we explore the challenges and opportunities in
identifying this elusive stellar population via the HeII$\lambda$1640 in
$M_\star > 10^{7.5} ~ \mathrm{M_\odot}$ galaxies during the Epoch of
Reionization (EoR, $z \simeq 6 - 10$), using JWST/NIRSpec. With this aim in
mind, we combine cosmological dustyGadget simulations with analytical modeling
of the intrinsic HeII emission. While tentative candidates with bright HeII
emission like GN-z11 have been proposed in the literature, the prevalence of
such bright systems remains unclear due to significant uncertainties involved
in the prediction of the HeII luminosity. In fact, similar Pop III clumps might
be almost two orders of magnitude fainter depending on the underlying Pop III
model (e.g., with/without stellar mass loss and/or assuming different Pop
III-formation efficiencies in star-forming clouds). Moreover, up to $\sim 90
\%$ of these clumps might be missed with NIRSpec/MOS due to the limited FoV,
while this problem appears to be less severe with NIRSpec/IFU. We propose deep
spectroscopy targeting potential peripheral Pop III clumps around bright,
massive galaxies as a promising approach to achieve a clear detection of the
first stars.
