  We have constructed conserved $\mathcal{N}=2$ higher-spin supercurrents for
an arbitrary integer spin through the unconstrained superfield formulation of
$4D,\, \mathcal{N}=2$ massless higher-spin theories in the harmonic superspace.
The obtained supercurrents are gauge-invariant and determine consistent cubic
interactions in the \textit{gauge superfield} $\times$ \textit{supercurrent}
form for massless spin $\mathbf{s_1}$ and two massless spin $\mathbf{s_2}$
$\mathcal{N}=2$ supermultiplets. Such interactions and $\mathcal{N}=2$
supercurrents exist only for $\mathbf{s_1}\geq 2 \mathbf{s_2}$. These
supercurrents are the $\mathcal{N}=2$ supersymmetric extension of
Berends-Burgers-van Dam higher-spin currents and generalize the linearized
Bel-Robinson tensor. The relevant $\mathcal{N}=2$ supercurrents can be
considered as the descendants of the $\mathcal{N}=2$ primary supercurrent,
which has a simple universal structure. An important feature of our outcomes is
that, ultimately, all $\mathcal{N}=2$ supercurrents are built from the
$\mathcal{N}=2$ superfield strengths, which are constructed from the
unconstrained analytical higher-spin prepotentials.
