  We test the hypothesis whether high redshift QSOs would preferentially appear
in small groups or pairs, and if they are associated with massive, young
clusters. We carried out a photometric search for \Ly emitters on scales
$\lesssim 10 h^{-1}$ Mpc, in the fields of a sample of 47 $z\approx3$ known
QSOs. Wide and narrow band filter color-magnitude diagrams were generated for
each of the $6'.6\times6'.6$ fields. A total of 13 non resolved objects with a
significant color excess were detected as QSO candidates at a redshift similar
to that of the target. All the candidates are significantly fainter than the
reference QSOs, with only 2 of them within 2 magnitudes of the central object.
Follow-up spectroscopic observations have shown that 5, i.e., about 40% of the
candidates, are QSOs at the same redshift of the target; 4 are QSOs at
different z (two of them probably being a lensed pair at z = 1.47); 2
candidates are unresolved HII galaxies at z$\sim$0.3; one unclassified and one
candidate turned out to be a CCD flaw. These data indicate that at least 10% of
the QSOs at z$\sim$3 do have companions.
  We have also detected a number of resolved, rather bright \Ly Emitter
Candidates. Most probably a large fraction of them might be bright galaxies
with [OII] emission, at z$\approx$ 0.3. The fainter population of our
candidates corresponds to the current expectations. Thus, there are no strong
indication for the existence of an overdensity of \Ly galaxies brighter than m
$\approx$ 25 around QSOs at $z\approx$ 3.
