In order to receive holiday money from your A-kasse ("feriedagpenge"), you must be entitled to dagpenge at the time of your holiday. This means that you must meet the general conditions for entitlement to dagpenge.
Among other things this means, that you must be:
- available for the labour market
- have residence in Denmark
- have a sufficient residence and work permit
- stay in Denmark up to the start of your holiday
I know that these things should already be something that the A-kasse knows about you, because they pay dagpenge to you already. So I can not tell, why the A-kasse ask if you are a danish citizen.
When you have right to dagpenge then you also have right to feriedagpenge. The A-kasse can not set further conditions for you (because you are not a danish citizen) regarding your right to feriedagpenge. The right to feriedagpenge is something you have because you have had the right to receive dagpenge in the period where you earn feriedagpenge.
Anders Weber, www.a-kasser.dk