In this article, we introduce a notion of relative mean metric dimension with potential for a factor map π : (X, d, T ) → (Y, S) between two topological dynamical systems. To link it with ergodic theory, we establish four variational principles in terms of metric entropy of partitions, Shapira's entropy, Katok's entropy and Brin-Katok local entropy respectively. Some results on local entropy with respect to a fixed open cover are obtained in the relative case. We also answer an open question raised by Shi [23] partially for a very well-partitionable compact metric space, and in general we obtain a variational inequality involving box dimension of the space. Corresponding inner variational principles given an invariant measure of (Y, S) are also investigated.