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Research on robotic ostracism is still scarce and has only explored its effects on adult populations. Although the results revealed important carryover effects of robotic exclusion, there is no evidence yet that those results occur in child-robot interactions. This paper provides the first exploration of robotic ostracism with children. We conducted a study using the Robotic Cyberball Paradigm in a third-person perspective with a sample of 52 children aged between five to ten years old. The experimental study had two conditions: Exclusion and Inclusion. In the Exclusion condition, children observed a peer being excluded by two robots; while in the Inclusion condition, the observed peer interacted equally with the robots. Notably, even 5-year-old children could discern when robots excluded another child. Children who observed exclusion reported lower levels of belonging and control, and exhibited higher prosocial behaviour than those witnessing inclusion. However, no differences were found in children's meaningful existence, self-esteem, and physical proximity across conditions. Our user study provides important methodological considerations for applying the Robotic Cyberball Paradigm with children. The results extend previous literature on both robotic ostracism with adults and interpersonal ostracism with children. We finish discussing the broader implications of children observing ostracism in human-robot interactions.