I will quit my job before the school term starts in September. Do i need to inform the Migrationsamt/Kreisbüro to change my permit in order to study 1-year full-time program?

If so:
-What type of permit are they giving me?
-When I need to do my internship, i'll need to change again?! and it will only be a L because it may not be a long contract?

Are you EU or Non-EU?

It is in the thread title

totally missed that!

That's totally ok.

Yes, you need to inform them and you should get a one year student B permit.

Thank you for your answer.

It's a bit upsetting to replace a 5-year permit with 1-year.

You do not need to replace the permit you already have. Your current permit allows you to study as well and counts for C permit. Student permit years only count for C if they are immediately followed by 2 years on working or family reunion B permit.

Does it? I had regular requests to show that I was employed during my B. Even as an EU citizen. OP has a work permit.

As an EU, OP has a residence permit valid for 5 years which allows work, study and self employment so long as the conditions to revoke the permit are not met.

You may be asked to demonstrate what your current status is after 5 years upon renewal time but studying is not a valid reason to revoke an EU B permit.