Primordial magnetic fields (PMFs) can enhance matter power spectrum on small scales (≲ Mpc) and still agree with bounds from cosmic microwave background (CMB) and Faraday rotation measurements. As modes on scales smaller than Mpc have already become non-linear today, exploring PMFs' impact on small-scale structures requires dedicated cosmological simulations. Here, for the first time, we perform a suite of hydrodynamical simulations that take into account the different impacts of PMFs on baryons and dark matter. Specifically, in the initial conditions we displace particles according to the Lorentz force from PMFs. We also highlight the large theoretical uncertainty in the peak enhancement of the matter power spectrum due to PMFs, which was not considered in previous studies. We present halo mass functions and show that they can be accurately reproduced using Sheth-Tormen formalism. Moreover, we show that PMFs can generate galaxies with baryon fraction several times larger than the cosmic average at high redshifts. This is simply a consequence of the fact that PMFs enhance baryon perturbations, causing them to be larger than dark matter perturbations. We argue that this scenario could be tested soon by obtaining accurate estimates of the baryon fraction in high redshift galaxies.
