Journal of Neutrosophic and Fuzzy Systems JNFS 2771-6449 2771-6430 10.54216/JNFS https://www.americaspg.com/journals/show/2724 2021 2021 University of Debrecen, Department of Mathematical and Computational Science, Debrecen, Hungary Warshine Warshine University of Chinese Academy of Sciences, CAS, Mathematics Department, Beijing, China Lee Xu Faculty Of Science, Beirut Arab University, Beirut, Lebanon Josef Al Jumayel The 3-cyclic refined neutrosophic roots of unity are exactly the solutions of the Diophantine equation  in the 3-cyclic refined neutrosophic ring of integers . This paper is dedicated to finding all 3-cyclic refined neutrosophic Diophantine roots of unity, where it proves that there exist only three solutions for the case of odd order (n), and twelve different solutions for the case of even order (n). On the other hand, the group generated from all solutions will be classified as a finite abelian group with direct products of finite cyclic groups. 2024 2024 23 30 10.54216/JNFS.080103 https://www.americaspg.com/articleinfo/24/show/2724