As best I can tell (CNI IV, p. 78 - 87):
- the currency was likely the grosso as no coin of higher denomination was known to have been struck according to CNI, and I cannot find any recent examples of such (maybe that's not perfect logic, but it's the best I've got
- the date range for this currency could have been 1186 - 1441 after which the city came under Venetian rule and presumably the Venetian monetary system.
- the list of ruling authorities could be:
Commune (1186-1337)
Berardo Maggi, Lord (1298-1308)
Pandolfo Malatesta, Lord (1404-1421)
I realize this leaves some gaps (for example 1337-1421, when I think it was under Milanese rule) and some overlaps (1298-1308), but this is what we find in the attribution of coins in CNI and on acsearch.
Examples:
https://www.acsearch.info/search.html?id=3361290
https://www.acsearch.info/search.html?id=4599275
https://www.numisbids.com/n.php?p=lot&sid=5572&lot=67