In this paper, the Fisher information (FI), relevant to m-generalized order statistics (m-GOSs) and their concomitants of the shape-parameter of the Sarmanov family of bivariate distributions, is investigated. In addition, we study the concomitants of m-GOSs from this family. Furthermore, we look at how those concomitants were distributed collectively. The FI contained in the scale and shape parameters of the exponential and power function distributions, respectively, in concomitants of m-GOSs is obtained. A study of the asymptotic behavior of the concomitants of ordinary order statistics is also provided. Some versatile applications for this study are offered. As a final step, we examined a bivariate real-world data set for illustrative purposes.