In the present study, a new complex convolution operator is introduced in terms of the meromorphic formula of the generalized Mittag-Leffler functions (MLfs), namely R– function. By employing the subordination methodology, appropriate classes of admissible functions are considered as well as the dual features of the third-order(3rd-order) differential subordination and superordination for this new operator are discussed. As a sequel, the sandwich-type outcome is also examined.