I am more familiar with times earlier than the Late Empire, so I mostly have Early Imperial or Republican examples. I see u/Aestuosus already has posted one from a textbook. This, swearing by the immortal gods, is something that is in our sources, though it usually takes the form of "di immortales". Cicero uses this a lot, both in his speeches and letters, and I also found a few examples in early Roman comedy (Plautus and Terence).

However it was also common to swear by (semi-)divine heroes, most notably Hercules, Castor and Pollux. Strangely, in our texts "mehercule" is never used by women and "(m)ecastor" never by men. Aulus Gellius actually discusses this phenomenon (Attic Nights 11.6) and ascribes it to religious ceremony. Especially "mehercule" and its variants "hercule", "hercle" appears rather often, in comedy of course but also in Sallust's histories (Philippus' Speech 17), when Suetonius paraphrases the words of Caligula (Life of Caligula 34.2), and several times in Curtius Rufus as dialogue by Alexander the Great (6.13.17, for instance). It is also sometimes used outside of dialogues and quotes, some examples including Columella's treatise on agriculture (Preface, 17), and Pliny seeming to use "tam Hercules" in similar way (Natural History 7.39/129).

I did find examples of swearing by Jupiter, though almost exclusively in early comedies. Some variants include "O Jupiter", "Pro Jupiter" and "pro supreme Jupiter". A little closer to the period you are interested in, Juvenal in his second Satire mentions effeminate Romans (or rather their servants) swearing by Juno. In some older dictionaries I have seen this written as "ejuno", but I could not find this form in any ancient text.