The following is what I have found from looking at the various studies on the therapy.
After looking at studies related to a variety of mental health and personality difficulties, Masley et al. (2012) states that;
The culminative message (both from the popularity of this model and the medium-to-large effect sizes) is of a theory that has already demonstrated clinically effective outcomes in a small number of studies and that would benefit from ongoing research and development with complex client groups.
Specifically looking at personality disorders, Jacob, G. A., & Arntz, A. (2013) found that treatment based on this model has been found to be very effective in several studies.
Looking for specific personality disorders, Sempértegui et al. (2013) points out that the the existing efficacy studies show positive outcomes of schema therapy for Borderline Personality Disorder but further work is required to achieve full empirical support of the model and therapy.
However, a more sobering review comes from Taylor et al. (2017), who state that
Schema therapy has demonstrated initial significant results in terms of reducing EMS [early maladaptive schema] and improving symptoms for personality disorders, but formal mediation analytical studies are lacking and rigorous evidence for other mental health disorders is currently sparse.
Jacob, G. A., & Arntz, A. (2013). Schema therapy for personality disorders—A review. International Journal of Cognitive Therapy, 6(2), 171-185. https://doi.org/10.1521/ijct.2013.6.2.171
Masley, S. A., Gillanders, D. T., Simpson, S. G., & Taylor, M. A. (2012). A systematic review of the evidence base for schema therapy. Cognitive behaviour therapy, 41(3), 185-202. https://doi.org/10.1080/16506073.2011.614274
Sempértegui, G. A., Karreman, A., Arntz, A., & Bekker, M. H. (2013). Schema therapy for borderline personality disorder: A comprehensive review of its empirical foundations, effectiveness and implementation possibilities. Clinical psychology review, 33(3), 426-447. https://doi.org/10.1016/j.cpr.2012.11.006
Taylor, C. D., Bee, P., & Haddock, G. (2017). Does schema therapy change schemas and symptoms? A systematic review across mental health disorders. Psychology and Psychotherapy: Theory, Research and Practice, 90(3), 456-479. https://doi.org/10.1111/papt.12112