Can I limit the read / write access to a custom field to users or groups?
Nope.
See https://jira.atlassian.com/browse/JRA-1330 for discussions, reason why you can't do it, and LOADS of workarounds.
Including a plugin at https://marketplace.atlassian.com/plugins/com.quisapps.jira.jfs
You can use plugin: https://marketplace.atlassian.com/plugins/ru.mail.jira.plugins.groupeditfiedls
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