Thank you for sharing your question with the Wefugees Community!
Yes, you are right. In general, if you have the residence permit according to Section 28 (1) for at least 3 years, you may be entitled to receive the permanent residence permit ("Niederlassungserlaubnis"). As far as I know, you may also need to prove that your "subsistence is secure" (as it is said in Section 9 (2) sentence 2/German Residence Act), so that you are able to cover your costs of living and you are not dependent on social benefits; and secondly, that you possess a work permit (Section 9 (2) sentence 5).
Please have a look at the respective Section in the German Residence Act for further requirements and details:
§28 (2): "As a rule, the foreigner must be granted a permanent settlement permit if he has possessed a temporary residence permit for three years, the family unit with the German continues to exist in the federal territory, there is no public interest in expelling the foreigner and the foreigner has a sufficient command of the German language. Section 9 (2) sentences 2 to 5 shall apply accordingly. The temporary residence permit shall otherwise be extended as long as the family unit continues to exist."
I hope this helps and please feel free to get back to us with any further questions.
All the best,