I have found little credible substance to these Popes having heretical beliefs.<quoted text>
In fairness, I will research each of the following:
The first two popes in the third century, Zephyrinus and Callistus, were both accused of heresy* by Tertullian and also by St Hippolytus.
Marcellinus,Bishop of Rome (296 to 304),offered incense to the pagan gods. For this his name was afterwards omitted from official lists of popes.
Three of the next four popes seem to have assisted him, despite being already in Holy Orders, but all of them, including Marcellinus, are now revered as r saints.
Early in the fifth century Pope Zosimus accepted the Pelagian heresy and changed his mind only when obliged to do so by the Emperor. He then issued a document known as his Tractoria, which reversed his earlier position.'
Also in the twelfth century Pope Adrian VI declared Pope Celestine III a heretic for extending the conditions under which marriages could be dissolved.
Pope Marcellinus was accused of this heresy by Donatists, who were themselves heretics.
Pope Zosimus was deceived by a disgenuine retraction of Pelagian.When he was informed of the deception he then clarified and withdrew any backing of the Pelagian.
I found nothing on Pope Celestine III