The COVID-19 pandemic has increased social media usage significantly, highlighting its critical role in public statements, information dissemination, news propagation. In this study, we construct and evaluate a fractional-order toxicity contagion model with quarantine intervention in Twitter. The model incorporates different infected groups that account for toxicity intensity and its development, that is, moderate and high infected users, and it is used to investigate the influence of each user in the overall spread of toxic content. We have evaluated the post-free toxic equilibrium point, the reproduction number \((\mathcal {R}_0)\) , the existence-uniqueness solution, and the stability point. The model, which fits well to (#F*covid) hashtags data, is qualitatively analyzed to evaluate the impacts of different schemes for control strategies. Our findings reveal that the conventional model, which does not differentiate between infected groups, overestimates or underestimates the rate of change in the number of infectious users, resulting in a greater error rate. From analysis, implementing quarantine measures on social media platforms can bring long-term benefits with low risk, affirming platform safety. By quarantining moderate and high toxic active users, the resulting error rates were impressively low, measured at 0.0011 and 0.0012 for the respective groups of infected users. This study will assist network providers in identifying such users, thereby reducing toxic conversations.