We present a new measurement of the space density of high redshift ( z \simeq 3.0-4.5 ) , X–ray selected QSOs obtained by exploiting the deep and uniform multiwavelength coverage of the COSMOS survey . We have assembled a statistically large ( 40 objects ) , X–ray selected ( F _ { 0.5 - 2 keV } > 10 ^ { -15 } erg cm ^ { -2 } s ^ { -1 } ) , homogeneous sample of z > 3 QSOs for which spectroscopic ( 22 ) or photometric ( 18 ) redshifts are available . We present the optical ( color-color diagrams ) and X–ray properties , the number counts and space densities of the z > 3 X–ray selected quasars population and compare our findings with previous works and model predictions . We find that the optical properties of X–ray selected quasars are not significantly different from those of optically selected samples . There is evidence for substantial X–ray absorption ( log N _ { H } > 23 cm ^ { -2 } ) in about 20 % of the sources in the sample . The comoving space density of luminous ( L _ { X } \hbox { \raise 2.15 pt \hbox { $ > \lower 4.558 pt \hbox { $ \kern - 10.7 pt { \sim } $ } $ } } 10 % ^ { 44 } erg s ^ { -1 } ) QSOs declines exponentially ( by an e–folding per unit redshift ) in the z \sim 3.0–4.5 range , with a behavior similar to that observed for optically bright unobscured QSOs selected in large area optical surveys . Prospects for future , large and deep X–ray surveys are also discussed .