National pension exemption as student

Hey guys,

Sorry for the long paragraph. So, I studied at Shizuoka University from October 2017 and just graduated in October this year.
During my 1st year of studies, I submitted the application for national pension exemption and granted, but on my 2nd year since I busy with my research and all, I forgot to apply for the exemption.

Shortly after that, I keep receiving the payments although I thought it wasn't a big deal since I also received the payments on the 1st year even though I applied for an exemption and decide to just ignore it. But now that I have time to check, I realized that I received the payments from last year until February next year.

And for now, I work as a part-timer not more than 28 hrs/week since I'm still using my current student visa (will renew later) and my income is not much.

I still reside in Japan and will stay here for another few years. Also, I will start working a full-time job from April next year and I know they have different national pension but for now what should I do? Can I still apply for the exemption as a student or low income or just pay the pension?

sorry for my English as well. Thanks for the help.

you have graduated the school in Oct. 2019.
you will have a job in April 2020.
even if you have student status of expiry date of April 2020,, the status becomes invalid when you have graduated the school. (i.e. you can't have a renewal of student status, after you graduated the school.)
you need to enter another school to keep the status or get a job immediately to change the status from student to working.

also, you can't work in part-time, when you have graduated the school, even if you have a student status with work permission. (the permission is valid only when you attend the school.)