Abstract
The aim of this paper is to generalise the construction of 3-BiHom-Lie superalgebras. We provide some properties that can be lifted to their T*-extensions such as nilpotency, solvability and decomposition. We study representations, T-theta-extensions and T-theta*-extensions of 3-BiHomLie superalgebras and prove the necessary and sufficient conditions for a 2n-dimensional quadratic 3-BiHom-Lie superalgebra to be isomorphic to a T-theta*-extension.