Have a look at https://docs.atlassian.com/jira/REST/server/ which lists all the REST calls you can make.
From memory, there isn't one for "fields associated with project", because it's not a simple question. Do you mean by field context? What if the field configuration hides it? What if there are several contexts with different options? What if it's valid, but not on screen, or on a screen but hidden? Finally, fields:project is not how it works, it's fields:issuetype-in-project
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