Is there any Select List type field which is project specific and editable only from Jira Rest API ?

[Vishal Kharde]

We have a requirement in which we need a Select List type field which is project specific and should allow add/delete/edit only from Jira Rest API. 

[Joe Pitt]

When you create the custom fields you can select which project it pertains to. However, that doesn't keep a JIRA admin from adding it to another project. Even if they do you can give the field 'context' so the list only applies to a project or issue type. 

https://confluence.atlassian.com/adminjiraserver/configuring-a-custom-field-938847235.html 

As for only being updated in Rest I can't help there.