This paper proposes the first implementation of a self-stabilizing regular register emulated by $n$ servers that is tolerant to both mobile Byzantine agents, and \emph{transient failures} in a round-free synchronous model. Differently from existing Mobile Byzantine tolerant register implementations, this paper considers a more powerful adversary where (i) the message delay (i.e., $\delta$) and the period of mobile Byzantine agents movement (i.e., $\Delta$) are completely decoupled and (ii) servers are not aware of their state i.e., they do not know if they have been corrupted or not by a mobile Byzantine agent. The proposed protocol tolerates \emph{(i)} any number of transient failures, and \emph{(ii)} up to $f$ Mobile Byzantine agents. In addition, our implementation uses bounded timestamps from the $\mathcal{Z}_{13}$ domain and it is optimal with respect to the number of servers needed to tolerate $f$ mobile Byzantine agents in the given model.