Its certainly not the Oldest, but a nice example is the Donation of Constantine. This supposed Roman imperial decree said that emperor Constantine transferred power over Rome and the Western empire to the bishop of Rome (the Pope). This was later used to legitimize papal political authority, especially in the 13th century. However it was met with suspicion. It would take until the Renaissance for it to be proven a forgery by humanist Lorenzo Valla. Here is some nice further reading if you're interested.

There are many actual and suspected conspiracies in Roman history. Since you appear interested in the unconfirmed ones, here is one example concerning the death of emperor Augustus in the year 14.

Tacitus writes that Augustus' illness and eventual death were suspected to be caused by his wife Livia. The theory was that she wished her son Tiberius to inherit the throne and was afraid Augustus would change his mind and appoint another heir:

While these and like topics were discussed, the infirmities of Augustus increased, and some suspected guilt on his wife's part.

Read the rest of Tacitus' story here.

Does the First Catilinarian Conspiracy count?

The first Catilinarian conspiracy was a plot to murder the consuls of 65 BC and seize power. Historians consider it unlikely that Catiline would have been involved in the First Catilinarian Conspiracy or, indeed, that the conspiracy existed at all.

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