  We describe several families of primary linear supermultiplets coupled to
three-dimensional ${\cal N}=2$ conformal supergravity and use them to construct
topological $BF$-type terms. We introduce conformal higher-spin gauge
superfields and associate with them Chern-Simons-type actions that are
constructed as an extension of the linearised action for ${\cal N}=2$ conformal
supergravity. These actions possess gauge and super-Weyl invariance in any
conformally flat superspace and involve a higher-spin generalisation of the
linearised ${\cal N}=2$ super-Cotton tensor. For massless higher-spin
supermultiplets in (1,1) anti-de Sitter (AdS) superspace, we propose two
off-shell Lagrangian gauge formulations, which are related to each other by a
dually transformation. Making use of these massless theories allows us to
formulate consistent higher-spin supercurrent multiplets in (1,1) AdS
superspace. Explicit examples of such supercurrent multiplets are provided for
models of massive chiral supermultiplets. Off-shell formulations for massive
higher-spin supermultiplets in (1,1) AdS superspace are proposed.
