  The supertwistor and bi-supertwistor formulations for ${\mathcal N}$-extended
anti-de Sitter (AdS) superspace in four dimensions, ${\rm AdS}^{4|4\mathcal
N}$, were derived two years ago in arXiv:2108.03907. In the present paper, we
introduce a novel realisation of the ${\mathcal N}$-extended AdS supergroup
$\mathsf{OSp}(\mathcal{N}|4;\mathbb{R})$ and apply it to develop a coset
construction for ${\rm AdS}^{4|4\mathcal N}$ and the corresponding differential
geometry. This realisation naturally leads to an atlas on ${\rm
AdS}^{4|4\mathcal N}$ (that is a generalisation of the stereographic projection
for a sphere) that consists of two charts with chiral transition functions for
${\mathcal N}>0$. A manifestly $\mathsf{OSp}(\mathcal{N}|4;\mathbb{R})$
invariant model for a superparticle in ${\rm AdS}^{4|4\mathcal N}$ is proposed.
Additionally, by employing a conformal superspace approach, we describe the
most general conformally flat $\mathcal N$-extended supergeometry. This
construction is then specialised to the case of ${\rm AdS}^{4|4\mathcal N}$.
