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In this paper, we study the general form of three-point functions ofconserved current multiplets $S_{\alpha(k)}= S_{(\alpha_1 \dots \alpha_k)}$ ofarbitrary rank in four-dimensional ${\mathcal N}=1$ superconformal theory. Wefind that the correlation function of three such operators $\langle\bar{S}_{\dot{\alpha}(k)} (z_1) S_{\beta(k+l)} (z_2) \bar{S}_{\dot{\gamma}(l)}(z_3) \rangle$ is fixed by the superconformal symmetry up to a single complexcoefficient though the precise form of the correlator depends on the values of$k$ and $l$. In addition, we present the general structure of mixed correlatorsof the form $\langle \bar{S}_{\dot{\alpha}(k)} (z_1) S_{\alpha(k)} (z_2) L(z_3)\rangle$ and $\langle \bar{S}_{\dot{\alpha}(k)} (z_1) S_{\alpha(k)} (z_2)J_{\gamma \dot{\gamma}} (z_3) \rangle$, where $L$ is the flavour currentmultiplet and $J_{\gamma \dot{\gamma}}$ is the supercurrent.

Three-point functions of higher-spin spinor current multiplets in ${\mathcal N}=1$ superconformal theory