Serious augmented reality (AR) games are becoming an emerging digital solution to positively impact learning experiences of children born in the digital age. However, empirically tested design guidelines for AR-based serious games are still largely unexplored. Within this study, we examine the design guidelines by creating four serious AR games with different mechanisms inspired by psychological needs within self-determination theory, and then conduct four user studies. In the first study, we explored concepts of AR games by conducting participatory design sessions. In the secondary study, we examined how children respond to different types of interactions and feedback mechanisms in AR serious games along with 32 participants. Next, we analyzed the effect of social interactions in serious augmented reality games on children with 24 participants. Finally, we developed an AR game with four different versions and tested ways to immerse and play children with 81 participants in an AR fantasy world. Overall, this research examined the concepts, prototypes and results of integrating AR with serious games for children. We have created several SDT-inspired AR prototypes and generalized a set of design guidelines to support future related designs in AR-based serious games.