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Hi,
as an international (non-EEA) graduate it is only possible to receive Unemployment benefits according to the graduate rule, if you have right to stay and work in Denmark (work permit).
On what basis/scheme you have the work permit is not important, but for being relevant to talk about A-kasse the work permit must give you a generel right to work fulltime in Denmark, for instance work permit under the Establishment Card Scheme.
A work permit limited to a certain job or a certain amount of hours means that it is not relevant to apply for membership in an A-kasse. Because when the job is finished, you are not allowed to stay in Denmark, and therefor you can not receive unemployment benefits.
You must be aware that you can not get a work permit under the Establishment Card Scheme and at the same time receive Unemployment benefits or other kind of public assistance.
It is one of the requirements for getting visa under the Establishment Card Scheme that you dont receive Unemployment benefits as an graduate. And you must also be able to proove that you are able to support yourself during your first year in Denmark after your education.
Establishment Card is one of several ways that you can apply for and get work permit. You can read about the different schemes here:
https://www.nyidanmark.dk/en-GB/You-want-to-apply/Work.
There is no other way to get dagpenge, as long as you dont have work permit.
When you have a work permit that gives you a generel right to work fulltime in Denmark, it will be relevant to apply for membership in an A-kasse.
If you get the Establishment Card you are allowed to work in Denmark for 2 years.
You will have to qualify for unemployment benefits before you can apply for benefits. This means that you must work as an self-employed or in a normal paid job, for at least 1 year, before you can apply for unemployment benefits.
You can read more about the requirements here:
https://www.a-kasser.dk/benefits/
Best regards,
Anders Weber, www.a-kasser.dk