  Primordial magnetic fields (PMFs) play a pivotal role in influencing
small-scale fluctuations within the primordial density field, thereby enhancing
the matter power spectrum within the context of the $\Lambda$CDM model at small
scales. These amplified fluctuations accelerate the early formation of galactic
halos and stars, which can be observed through advanced high-redshift
observational techniques. Therefore, Stellar Mass Density (SMD) observations,
which provide significant opportunities for detailed studies of galaxies at
small scales and high redshifts, offer a novel perspective on small-scale
cosmic phenomena and constrain the characteristics of PMFs. In this study, we
compile 14 SMD data points at redshifts $z > 6$ and derive stringent
constraints on the parameters of PMFs, which include the amplitude of the
magnetic field at a characteristic scale of $\lambda=1\,{\rm Mpc}$, denoted as
$B_0$, and the spectral index of the magnetic field power spectrum, $n_{\rm
B}$. At 95\% confidence level, we establish upper limits of $B_0 < 4.44$ nG and
$n_{\rm B} < -2.24$, along with a star formation efficiency of approximately
$f_*^0 \sim 0.1$. If we fix $n_{\rm B}$ at specific values, such as $-2.85$,
$-2.9$, and $-2.95$, the 95\% upper limits for the amplitude of the magnetic
field can be constrained to 1.33 nG, 2.21 nG, and 3.90 nG, respectively.
Finally, we attempt to interpret recent early observations provided by James
Webb Space Telescope (JWST) using the theory of PMFs, and find that by
selecting appropriate PMF parameters, it is possible to explain these results
without significantly increasing the star formation efficiency.
