Aims. The true nature of primordial magnetic fields (PMFs) and their role in the formation of galaxies remains elusive. To shed light on these unknowns, we investigated 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. Methods. We used the magneto-hydrodynamics code RAMSES to generate multiple new zoom-in simulations for eight different host halos of dwarf galaxies across a wide luminosity range of 103 − 106 L⊙. These halos were selected from a ΛCDM cosmological box, tracking their evolution down to redshift z = 0. We explored a variety of primordial magnetic field (comoving) strengths of Bλ ranging from 0.05 to 0.50 nG. Results. We find that magnetic fields in the interstellar medium not only modify star formation processes in dwarf spheroidal galaxies, but these fields also entirely prevent the formation of stars in less compact, ultra-faint galaxies with halo masses and stellar masses below, respectively, ∼2.5 × 109 and 3 × 106 M⊙. 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 107 to 109 M⊙ in the ΛCDM+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 of z > 9. We investigated the evolution of various energy components and demonstrated that magnetic fields with an initial strength of Bλ ≥ 0.05 nG exhibit a strong growth of magnetic energy, accompanied by a saturation phase that begins soon after the growth phase. These trends persist consistently, regardless of the initial conditions or whether it is the classical ΛCDM model or ΛCDM modified by PMFs. Lastly, we investigated the impact of PMFs on the present-time observable properties of dwarf galaxies, namely: the half light radius, V-band luminosity, mean metallicity, and velocity dispersion profile. We find that PMFs with moderate strengths of Bλ ≤ 0.10 nG show an impressive agreement with the scaling relations of the observed Local Group dwarfs. However, stronger fields lead to larger sizes and higher velocity dispersions.