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 $z>12$.
