Quantum N=2 super-W-3((2)) algebra in superspace

We discuss the N = 2 extension of Polyakov-Bershadsky W-3((2)) algebra with the generic central charge, c, at the quantum level in superspace. It contains, in addition to the spin-1 N = 2 stress tensor, the spins 1/2, 2 bosonic and spins 1/2, 2 fermionic supercurrents satisfying the first-class nonlinear chiral constraints. In the c --> infinity limit, the ''classical'' N = 2 W-3((2)) (2) algebra is recovered.