During an emperor's reign, were coins (i.e. sestertii) minted the year they became emperors, the year they stopped being emperors, or right in the middle?
It is known that coins were minted in the first years, if not the first, of the new Emperor's reign. The populace often learned of a new Roman Emperor when coins appeared with the new Emperor's portrait. Some of the emperors who ruled only for a short time made sure that a coin bore their image; Quietus, for example, ruled only part of the Roman Empire from 260 to 261 AD, and yet he issued two coins bearing his image.
Roman imperial coins span a period of over 500 years beginning, technically, with the first issues following the Roman Senate's bestowment of the title Augustus on Octavian in 27 BC and gradually blending into what will become known as the Byzantine culture in the 6th century.
During this entire period almost every coin minted within the borders of the Roman empire will feature a ruler from the present imperial court as a portrait on the obverse of each and every coin. This trait alone is so consistent that it becomes an easily identifiable signature which can be used to quickly rule out the majority of other ancient coin-making cultures.
Sources and suggested reading:
Roman Coins and Public Life Under the Empire: E. Togo Salmon Papers II, edited by George M. Paul, Michael Ierard