  Within the framework of (2,0) anti-de Sitter (AdS) supersymmetry in three
dimensions, we propose a multiplet of higher-spin currents. Making use of this
supercurrent, we construct two off-shell gauge formulations for a massless
multiplet of half-integer superspin $(s+\frac 12)$, for every integer $s>0$. In
the $s=1$ case, one formulation describes the linearised action for (2,0)
anti-de Sitter supergravity, while the other gives the type III minimal
supergravity action in (2,0) AdS superspace, with both linearised supergravity
actions originally derived in arXiv:1109.0496. The constructed massless actions
are then used to formulate topologically massive higher-spin supermultiplets in
(2,0) AdS superspace. Our results admit a natural extension to the case of
$S^3$.
