Welcome back to the Wefugees Community and thank you for reaching out to us again.
As mother of a German child, privileged requirements apply to you for obtaining the permanent settlement (Niederlassungserlaubnis). Please see, for instance, this website for a full list of the conditions (in this case, exemplary for residents of Berlin). One privilege is, that you can apply for the permanent settlement already after holding the residence permit according to section 28 of the German Residence Act for three years. However, the immigration office is still asking for proofs that your livelihood is secured, or at least predominantly financed by yourself (independent of Jobcenter/social money). The respective calculations are quite complicated (examples here) and I recommend you to contact a counselling office to support you in this.
I am afraid though, that a minijob will not be sufficient for the time being to cover the expenditures of you and your family. The immigration office also looks at the applicant's perspectives and the chances to secure the livelihood in the near future.
Nevertheless, I am sure that you will have good chances to obtain the Niederlassungserlaubnis once you finished your Ausbildung and work as qualified employee.
I hope this helps and please don't hesitate to get back to us with any further questions.
All the best,