  The true nature of primordial magnetic fields (PMFs) and their role in the
formation of galaxies still remains elusive. To shed light on these unknowns,
we investigate their impact by varying two sets of properties: (i) accounting
for the effect of PMFs on the initial matter power spectrum, and (ii)
accounting for their magneto-hydrodynamical effects on the formation of
galaxies. By comparing both we can determine the dominant agent in shaping
galaxy evolution. We use the magneto-hydrodynamics code RAMSES, to generate
multiple zoom-in simulations for eight different host halos of dwarf galaxies
across a wide luminosity range of $10^3-10^6\,L_{\odot}$. We explore a variety
of primordial magnetic field (comoving) strengths ranging from $0.05$ to
$0.50\,\mathrm{nG}$. We find magnetic fields in the interstellar medium not
only modify star formation in dwarf spheroidal galaxies but also completely
prevent the formation of stars in less compact ultra-faints with halo mass and
stellar mass below $\sim 2.5\cdot10^9$ and $3\cdot10^6\,M_{\odot}$,
respectively. At high redshifts, the impact of PMFs on host halos of dwarf
galaxies through the modification of the matter power spectrum is more dominant
than the influence of magneto-hydrodynamics in shaping their gaseous structure.
Through the amplification of small perturbations ranging in mass from $10^7$ to
$10^9\,M_{\odot}$ in the $\Lambda$CDM$+$PMFs matter power spectrum, primordial
fields expedite the formation of the first dark matter halos, leading to an
earlier onset and a higher star formation rate at redshifts $z>12$.
