I have a choice field with 3 choices: Approved, Rejected, Resubmit
I want one SharePoint group to see Approved and Rejected and another SharePoint group to see only resubmit option.
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If you are using SP 2013 (or later) and you need this restriction only on the Web UI, the simplest solution I can imagine is to create a custom rendering template for your field via JSLink.
JSLink and display templates are a quite huge topic, but you find a very good overview of them here.