Constantinople had a population of "Latins" that numbered multiple tens of thousands. (source for that)
Latins were Christians who took the side of the Bishop of Rome (the Pope) against the other 4 members of the Pentarchy in the East during the Great Schism. They were likely known as Latina because of their association with the City of Rome and also because of the usage of Latin in Catholic worship.
In Western lands that stood with Rome on the questions of Papal authority/Petrine supremacy were there any noticeable populations of people who supported the east (the Patriarchs of Constantinople, Antioch, Jerusalem and Alexandria) in the schism and worshiped in the Byzantine Rite? If so, where were they and what troubles did they face if any?
I'm not sure what period are you interested in.
If you are thinking on Middle Ages, the most western positioned Orthodox country was Kingdom of Bosnia, I believe. I also think that there weren't any Orthodox Christian populations in ''western'' countries.
Later population, mostly Serbian, migrated to Austria and settled as far as what is today Dalmatia and around Trieste. So it can be said that those people lived under a state which was oriented towards Rome. But we are talking now about 16th and 17th century.