Yes. Tick the groups that may see it when you edit the field. Everybody else will not see it on the record, in the list, in the API, or in search results.

When you edit a field there is a list of groups under Only these groups may see it. Tick none and everybody sees it; tick some and only those groups do.

A hidden field is removed before the page is built rather than hidden on it, so it does not appear in the page source either. It is also kept out of the search index entirely, which means nobody can find the record by searching for a word that only appears in a restricted field.

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