The usual fix for this one is to remove the field from "edit" screens, add it to a "transition" screen, and have "edit <custom field>" as a workflow transition, to which you add "only role X can use this" as a condition.
At the moment it's not possible to achieve this level of restrictions within JIRA built-in tools solely.
However, you can try this plugin as it might be exactly what you are looking for:
Also, please check https://jira.atlassian.com/browse/JRA-1330 for discussions, reasons why you can't do it, and LOADS of workarounds.
I hope it helps!
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