  We study two geometric properties of reproducing kernels in model spaces
$K\_\theta$where $\theta$ is an inner function in the disc: overcompleteness
and existence of uniformly minimalsystems of reproducing kernels which do not
contain Riesz basic sequences. Both of these properties are related to the
notion of the Ahern--Clark point. It is shown that "uniformly minimal
non-Riesz"$ $ sequences of reproducing kernelsexist near each Ahern--Clark
point which is not an analyticity point for $\theta$, whileovercompleteness may
occur only near the Ahern--Clark points of infinite orderand is equivalent to a
"zero localization property". In this context the notion ofquasi-analyticity
appears naturally, and as a by-product of our results we give conditions in
thespirit of Ahern--Clark for the restriction of a model space to a radius to
be a class ofquasi-analyticity.
