The painting in the Cleveland Museum of Art is likely a studio copy of the original, which was displayed in the church of Santa Maria degli Angeli, Rome.
In the latter, both Peter and Paul are present in Rome; Simon Magus to astound the apostles with his power to levitate, flies off a high structure, but Peter, with his prayers, is able to confound the demons holding Simon aloft, and the sorcerer falls to his death.
The emperor is flanked by a statue of Hercules, and a pell-mell of legionnaire standards, fasces, and a banner with the abbreviation SPQR.
The topic was appropriate for the Basilica of St Peter, specially since it was a demonstration of the power of the First Pope against nonconforming and pagan ideas.
Batoni had altered a previous model of the scene by Francesco Vanni, this time making the figures grander.