What does Caesōnius mean in Latin?

Caesōnius, a proper noun, means “a Roman nomen gentile, gens or "family name" famously held by”.

What is the genitive of Caesōnius?

The genitive singular is Caesōniī. Caesōnius is masculine, second declension.

In classical Latin, [kae̯ˈsoː.ni.ʊs]; in ecclesiastical (church) Latin, [t͡ʃeˈs̬ɔː.ni.us].

proper noun · masculinesecond declension

Caesōnius m sg (genitive Caesōniī or Caesōnī)

Classical[kae̯ˈsoː.ni.ʊs]Ecclesiastical[t͡ʃeˈs̬ɔː.ni.us]

Caesōnĭus, a,

I. name of a Roman gens. —So,

I. M. Caesonius, œdile with Cicero, Cic. Att. 1, 1, 1; 1, 12, 11; Cic. Verr. 1, 10, 29. —

II. Caesonius Paetus, consul under Nero, Tac. A. 14, 29.—Hence, Caesōnĭānus, a, um, adj., Col. 1, 4, 1.—

III. Milonia Caesonia, mistress and afterwards wife of Caligula, Suet. Calig. 25; Juv. 6, 616.

From Caesō.