The Romans used something called AUC, ab urbe condita, meaning ‘year since the founding of the City’ (ie. Rome) which we generally take to be 753BC, though there’s a lot of debate about that. So AUC 1000 would’ve been roughly the early 3rd century AD. The AUC system was used right down to the early Byzantine era I think (?), with the Anno Domini (AD) system developed in the 6th century.

The Romans also used consular years to mark dates, so whichever two consuls held rank that year gave their name to that particular consular year. This started from the republican period and continued into the imperial period. I’m not sure when exactly this stopped being used, but technically it could’ve been used right down to the end of the antique period.

The Achaemenid Persians as far as we know never wrote down any narrative history, so we have very little idea how they dated events. Probably they followed ancient Near Eastern convention and used regnal years (ie. in the first year of the reign of King so and so). The Greek historians like Herodotus, Ctesias, Plutarch seemed to have phrased Persian dates in regnal years.

Come to think of it I don’t think the Sassanid Persians wrote down any narrative history either, though the later Shahnameh kind of counts. I haven’t scoured through it to find dating conventions but from what I can tell it’s regnal years as well.