Three-point functions of a superspin-2 current multiplet in 3D, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="script">N</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:math> superconformal theory

We consider $\mathcal{N}=1$ superconformal field theories in three dimensions possessing a conserved current multiplet ${\mathcal{F}}_{({\ensuremath{\alpha}}_{1}{\ensuremath{\alpha}}_{2}{\ensuremath{\alpha}}_{3}{\ensuremath{\alpha}}_{4})}$, which we refer to as the superspin-2 multiplet. At component level it contains spin-2 different from energy-momentum tensor and fermionic higher-spin of spin $5/2$. Using superspace formulation, calculate correlation functions involving $\mathcal{F}$, focusing particularly on three-point function $?\mathcal{F}\mathcal{F}\mathcal{F}?$. After imposing constraints arising conservation equations invariance under permutation points, find that parity-even parity-odd sectors this are each fixed up single coefficient. The presence contribution is rather nontrivial, there an apparent tension between supersymmetry existence structures.