The trial period:
in the "trial" period it will be possible for you to have supplementary benefits. In the trial period you only have one days quitting notice, and therefore meet the requirement for being available for the labour market.
After the trial period:
It is unusual to have 3 months quit notice for at short term temporary work as yours. Are you sure you have 3 months notice? So you need to say 3 months before if you want to quit the job?
It is not only your employer who have 3 months?
If you really have 3 months from your side, then you need the "frigørelsesattest". If you want to have Unemployment benefits ("dagpenge"), one of the conditions is that you are available for the labour market, meaning you can take over a new job with one day notice. This requirement also applies for "supplementary benefits".
But this is not possible if you can not quit your current job with one day notice.
Only if your reduced working time can be placed at any time (by your self) so that working time does not prevent you from taking a new job, you can get supplementary benefits without the need of an "frigørelsesattest". This applies, for example if you organize your work yourself and do not have a duty to perform it at specific times.
Otherwise, there is no other way to get supplementary benefits after the trial period. The requirments are clear and you need to meet all requirements.
Please comment in this forum, if you have further comments.
Anders Weber, www.a-kasser.dk