While over a hundred articles discuss second-order differential inequalities and subordinations in the complex plane, very few address the relatively unexplored classes of third-order fuzzy differential subordination and superordination. This paper builds upon the recently proposed concepts of third-order fuzzy differential subordination and superordination, which are developed using a linear operator and a meromorphic function. By applying techniques based on the fundamental notion of admissible functions, we begin by defining the appropriate class of such functions necessary for deriving new results in third-order fuzzy differential subordination. The study reveals the establishment of sandwich-type theorems, linking these new findings with established methods in third-order fuzzy differentiation and superordination theory.