Social network platforms (SNP) rely heavily on user-generated content to attract users, yet they have limited control over content provision, which leads to misinformation. As countermeasures, SNPs have implemented policies to notify users by tagging the content and influencing users' responses to the tagged content. The population-level response creates a social nudge to the content provider that encourages it to supply more authentic content. Yet, when designing tags to leverage social nudges, SNP must be cautious about misdetection, which impairs its ability to create social nudges. We establish a Bayesian persuaded branching process to study SNP's tagging policy design under misdetection. Misinformation circulation is modeled by a multi-type branching process, where users are persuaded through tags to give positive/negative comments that influence misinformation spread. When translated into posterior belief space, the SNP's problem is reduced to an equality-constrained optimization, the optimal condition of which is given by the Lagrangian characterization. The key finding is that SNP's optimal policy is transparent tagging, albeit misdetection, which nudges the provider not to generate misinformation.