Zosimus (reigned 417-418) was approached by Caelestius, who brought a profession of faith from Pelagius for the Pope’s examination. Zosimus examined Caelestius and the profession and found nothing heretical in them. He said the African bishops’ condemnation of Pelagius and Caelestius had been hasty and instructed Africans with charges against them to appear in Rome for further investigation.
This prompted outrage among the African bishops since they considered the Pelagian controversy to have been closed by Zosimus’s predecessor, Innocent I. Zosimus responded by stressing the primacy of the Roman see and by explaining to them that he had not settled the matter definitively and that he did not intend to do so without consulting them. He said that his predecessor’s decision remained in effect until he had finished investigating the matter.
The bishops provided Zosimus with additional evidence against Pelagius, and the Pope condemned Pelagianism. His initial assessment had been a tentative judgment, based on partial evidence. He did not issue a definitive judgment, much less a doctrinal definition, as indicated by the fact he asked for additional evidence to be sent to Rome. The case of Zosimus thus does not touch the doctrine of papal infallibility.
For more on this topic, see this article.