  Off-shell higher spin N=2 supermultiplets in three spacetime dimensions (3D)
are presented in this paper. We propose gauge prepotentials for higher spin
superconformal gravity and construct the corresponding gauge-invariant field
strengths, which are proved to be conformal primary superfields. These field
strengths are higher spin generalisations of the (linearised) N=2 super-Cotton
tensor, which controls the superspace geometry of conformal supergravity. We
also construct the higher spin extensions of the linearised N=2 conformal
supergravity action. We provide two dually equivalent off-shell formulations
for massless higher spin N=2 supermultiplets. They involve one and the same
superconformal prepotential but differ in the compensators used. For the lowest
superspin value 3/2, these higher spin series terminate at the linearised
actions for the (1,1) minimal and w=-1 non-minimal N=2 Poincar\'e supergravity
theories constructed in arXiv:1109.0496. Similar to the pure 3D supergravity
actions, their higher spin counterparts propagate no degrees of freedom.
However, the massless higher spin supermultiplets are used to construct
off-shell massive N=2 supermultiplets by combining the massless actions with
those describing higher spin extensions of the linearised N=2 conformal
supergravity. We also demonstrate that every higher spin super-Cotton tensor
can be represented as a linear superposition of the equations of motion for the
corresponding massless higher spin supermultiplet,with the coefficients being
higher-derivative linear operators.
