In an observational study, the propensity score is widely used to adjust for confounding bias when the treatment is binary and, to some extent, for categorical and continuous treatments. This study introduced the application of count treatments to causal inference on ordinal outcomes. We compared different methods, including maximum likelihood for the family of count models, generalized boosted model (GBM), and covariate balancing propensity score (CBPS), to estimate generalized propensity score (GPS). In the comparison, we used effective sample size in combination with confounders balancing power and efficiency of treatment effect estimation. In the treatment effect estimation, confounders’ bias was controlled using inverse probability of treatment weighting (IPTW). Two outcome models, including marginal structural modeling and considering GPS as a covariate, were compared in terms of the efficiency of treatment effect estimation. To reduce the influence of extreme IPTW, we trimmed the GPS at the 1st and 99th percentiles. We also applied path-specific effects estimation under sequential mediators while estimating the count treatments effect on the ordinal outcomes. In this case, a composite weighting method was introduced to estimate path-specific effects under sequential mediators to weight each component of the structural equation modeling of mediators and outcome. The first mediator model was weighted by IPTW generated from the treatment model; the second mediator model was weighted by the composite IPTW generated from the treatment and the first mediator model; and the outcome model was weighted by the composite IPTW generated from the treatment and mediators. The proposed weighting method was compared with simulation-based G-computation in terms of treatment effect estimation. For real-life data, we used the number of antenatal care visits (ANC) as a count treatment and age-specific childhood vaccination as an ordinal outcome. We also used a simulation study to compare the proposed models in the study. The result shows that GBM-based weighting is better than other methods to maintain a high effective sample size and efficient count treatment effect estimation while having equivalent performance with other methods in terms of covariate balancing. Marginal structural modeling produced better treatment effect estimation than using GPS as a covariate. The proposed weighting method and G-computation based on simulation have comparable performance in terms of treatment effect estimation, despite the fact that the proposed weighting method is computationally efficient. The number of ANC visits has a positive effect on the likelihood of timely childhood vaccination. In viii the meantime, the effect was mediated by institutional delivery and newborn postnatal care, though the direct effect of ANC visits is higher than the indirect effects.