Please note that Mommsen uses the AUC chronology (Ab Urbe Condita), i.e. from the founding of the City of Rome. You can use this reference table to have the B.C. dates
From: The History of Rome, by Theodor Mommsen
Translated with the sanction of the author by William Purdie Dickson
This mode of administration appears to have been at first extended also to the territories taken from Carthage, and Sicily and Sardinia to have been governed for some years by quaestors under the superintendence of the consuls; but the Romans must very soon have become practically convinced that it was indispensable to have superior magistrates specially appointed for the transmarine regions. As they had been obliged to abandon the concentration of the Roman jurisdiction in the person of the praetor as the community became enlarged, and to send to the more remote districts deputy judges,(4) so now (527) the concentration of administrative and military power in the person of the consuls had to be abandoned.
4. Cf. III. VIII. Changes in Procedure
For each of the new transmarine regions--viz. Sicily, and Sardinia with Corsica annexed to it--there was appointed a special auxiliary consul, who was in rank and title inferior to the consul and equal to the praetor, but otherwise was--like the consul in earlier times before the praetorship was instituted--in his own sphere of action at once commander-in-chief, chief magistrate, and supreme judge. The direct administration of finance alone was withheld from these new chief magistrates, as from the first it had been withheld from the consuls;(5) one or more quaestors were assigned to them, who were in every way indeed subordinate to them, and were their assistants in the administration of justice and in command, but yet had specially to manage the finances and to render account of their administration to the senate after having laid down their office.
5. Cf. II. I. Restrictions on the Delegation of Powers
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Reference address : https://www.ellopos.net/elpenor/rome/3-03-extension-italy.asp?pg=10