[Fixed]-API access authentication/application key (django/nginx/gunicorn)

There are many authentication methods beside of session/cookie based ones. For your case I will suggest simple token authentication. Just save same token in your django app and external app and on each request from external app to django, send additional header:

Authentication: Token YOUR_TOKEN_KEY

Now all you need to do in django is to fetch that token and check if it matches one saved locally.

If you want more auth options for API, check Django Rest Framework documentation.