Dear @Melhopenot,
Welcome back to the Wefugees Community and thank you for reaching out to us again.
I am not a lawyer and I am not very experienced with the "Asylfolgeantrag" (subsequent asylum application) either. However, I read in this expert article (page 61 and following; unfortunately only in German) that you may have only one week to appeal against the rejection. The BAMF can reject your application in two different ways: It may reject it as "inadmissible" without even assessing the content of your application or it is actually checking your grounds for re-applying but at the end decides to reject it. The article highlights that it is very important to have legal support by lawyer latest at the point when your subsequent asylum application is rejected and you want to appeal since only then there may be a chance to suceed with it. If you file a second "Folgeantrag" and it is rejected as "inadmissible" again, the authorities may indeed issue a ban to re-enter Germany.
However, in the most cases, leaving the country vouluntarily (without getting deported) is preventing a re-entry ban and there might be a chance to come back with a visa (if conditions are met). To prepare this procedure, I highly recommend to get support at a migration counselling office and/or a lawyer.
Do you agree with my explanations dear @mbeon-fardeen?
I hope this helps and please don't hesitate to get back to us with any further questions.
All the best,
Meike