Hi,
it is correct what your A-kasse have told you. You can not get dagpenge from A-kasse as long as you are sick.
When you are not sick anymore, you can apply for dagpenge in your A-kasse.
Period with sickness (over 160,33 hours) will extend the period in which the A-kasse will look back in time (3 years) to see if you meet the income requirement for being eligible for dagpenge.
So if you meet the requirements now, you will probably also do after the period with sickness.
However, the A-kasse must assess whether you are healthy and available for the labor market. This means that as a full-time insured you must be able to take over work for 37 hours a week with a day’s notice, or 30 hours if you are part-time insured.
Best regards,
Anders Weber, A-kasser.dk