Hi,
If you are a third-country citizen and fulfil the conditions for residence as a family member to an EU citizen, you have the same rights to reside and work in Denmark as the EU citizen.
This means that you can meet one of the requirements for being eligible for Unemployment benefits (in Danish: dagpenge) – the availability requirement (you can take any job with one day notice).
For being eligible for dagpenge, you must also meet the other requirements, which you can read about here:
https://www.a-kasser.dk/requirements/
Depending of your wifes grounds for residence, your right of residence, or the right of residence of your wife, could be affected if one of you – or you both – receives benefits regulated by the Act on Active Social Policy, such as cash benefits. However Unemployment benefits (“dagpenge”) is NOT covered by the Act on Active Social Policy.
Hence, receiving dagpenge or state study grants (in Danish: SU) does not affect your right to reside in Denmark.
Best regards,
Anders Weber, A-kasser.dk