We study the fermionic T-duality symmetry of integrable Green-Schwarz sigma-models on AdS backgrounds with Ramond-Ramond  fluxes and with even number of supersymmetries. The backgrounds are semi-symmetric spaces induced by a Z₄ automorphism of superconformal algebras (SCA's). We find general conditions for T-self-duality of the backgrounds and classify all backgrounds satisfying them. We find new classes of T-self-duality directions and give the general transformation of the flat-connection and monodromy matrix.