We develop a three-dimensional $\mathcal{N}=4$ theory of rigid supersymmetry describing the dynamics set hypermultiplets $(\Lambda^{\alpha\alpha'\dot{\alpha}'}_I,\,\phi^{\alpha A}_I)$ on curved AdS$_3$ worldvolume background, whose is captured by supergroup ${\rm D}^2(2,1;\, \boldsymbol{\alpha})$. To unveil some remarkable features this model, we perform two twists, involving SL$(2,\mathbb R)$ ...