  We recently predicted the existence of random primordial magnetic fields
(RPMF) in the form of randomly oriented cells with dipole-like structure with a
cell size $L_0$ and an average magnetic field $B_0$. Here we investigate models
for primordial magnetic field with a similar web-like structure, and other
geometries, differing perhaps in $L_0$ and $B_0$. The effect of RPMF on the
formation of the first galaxies is investigated. The filtering mass, $M_F$, is
the halo mass below which baryon accretion is severely depressed. We show that
these RPMF could influence the formation of galaxies by altering the filtering
mass and the baryon gas fraction of a halo, $f_g$. The effect is particularly
strong in small galaxies. We find, for example, for a comoving $B_0=0.1\muG$,
and a reionization epoch that starts at $z_s=11$ and ends at $z_e=8$, for
$L_0=100\,\text{pc}$ at $z=12$, the $f_g$ becomes severely depressed for
$M<10^7\msun$, whereas for $B_0=0$ the $f_g$ becomes severely depressed only
for much smaller masses, $M<10^5\msun$. We suggest that the observation of
$M_F$ and $f_g$ at high redshifts can give information on the intensity and
structure of primordial magnetic fields.
