You can see the following paper:

S. Majid, "Quantum Double for Quasi-Hopf Algebras",Letters in math. phys., 45, Number 1 , pages 1-9 (1998).

You can see the following papers:

S. Majid, "Quantum Double for Quasi-Hopf Algebras",Letters in math. phys., 45, Number 1 , pages 1-9 (1998).

C. A. S. Young, R. Zegers. Triangular quasi-Hopf algebra structures on certain non-semisimple quantum groups, Commun. Math. Phys. 298, 585-611 (2010).