as I understand you, you have been living in Denmark since august 2016, but are still hired by an employer in Belgium, from where you have been on parental leave for some time now, and until may this year.
As an EU citizen it is possible to transfer your earned rights - this means your insurance periods and working periods from Belgium to another EU country.
So this is possible only if you at the moment are member of/paying to Unemployment Insurance in Belgium.
And when moving to Denmark, you must be aware that Denmark is one of the few countries who have some special requirements for being able to transfer these earned rights to the danish Unemployment Insurance Fund (A-kasse).
We have a special article about these requirements. You can read it here:
As you can see here you must apply for membership of an danish A-kasse within 8 weeks after you ceased to be insured in another EU country. This would normally be 8 weeks after moving to Denmark.
In Denmark we have a special additional requirement saying that you - if you have not been member of a danish A-kasse within the last 5 years - must within the 8 weeks begin work in Denmark of at least 296 hours over 12 weeks / 3 months.
What happens if the 8-week requirement is exceeded?
If the 8-week deadline for commencement of work or application for admission is exceeded, insurance periods from the other EEA country can not be included. This means that you will be entitled to Unemployment benefits ("Dagpenge") only after 1 year of membership of a danish A-kasse. Working periods from the other EEA country may be included, even though the 8-week deadline is exceeded.
Extension of the 8-week deadline for starting work in Denmark
The A-kasse may extend the 8-week deadline and the deadline for fulfilling the requirement for work of up to 2 years. This can happen in case of documented illness, maternity leave, parental leave or childcare leave.
I have not heard about situation similar to yours before - where it seems you have been living in Denmark for over 1,5 years and still is employed in Belgium and member of the Belgium Unemployment Insurance.
So therefor we also recommend you to contact an A-kasse here in Denmark before you apply for membership, and ask them about the possibilty to transfer your rights.
Please comment, if you need further information.