Hi,
the relevant law (Bekendtgørelse om betaling af medlems- og efterlønsbidrag til en a-kasse, §8) states that the condition for free membership is that you do not have an total yearly income (from work, SU etc.) that exceeds the DKK 226,392 (2019) or DKK 228,996 (2020).
The A-kasse will use the 2019-limit when they decide if you have met the conditions for free membership in 2019, and similar for 2020.
If you graduate in june 2019, the A-kasse will calculate whether you meet the requirements for free membership from january to june, by doing a proportionate calculation. So for exsample if you graduate 1st july 2019, your maximum income for the period 1/1-1/7 2019 must not exceed 226,392/2.
But in generel, the A-kasse look at a full calender year, so its your income for a full calender year that is relevant. If your income (incl. SU) for 2019 exceeded the maximum, then you do not meet the reguirements for free membership for all 2019, and you will have to pay membership fee for the full 2019.
The A-kasse will make a calculation every year, and you can only be required to pay fee for the particular year where you income have exceeded the maximum allowed. So you can not be required to pay for more than 1 year, if you only have exceeded the maximum in 1 year.
You can not "answer wrong" to the A-kasse. You have to tell them everything. Its not possible to hide income from the A-kasse, because they have access to the income-register, and will check that its correct what you tell them.
You must trust the A-kasse in this case, they will not try to cheat you, and you can not say anything wrong. Let me know if you have further questions.
Best regards,
Anders Weber, www.a-kasser.dk