Good morning dear Bona,
thank you for sharing of your question in the community. First of all I would like you share the translation of the Text in English (maybe you have already translated):
In accordance with Section 16a (1) sentence 2 of the Residence Act, a residence permit for another purpose of residence may only be issued for the purpose of qualified vocational training, the exercise of employment as a specialist, the exercise of employment with pronounced practical knowledge in accordance with Section 19c (2) or in cases of a legal claim will. If you want to pursue other / other employment, you need a corresponding national visa, which you can apply for in your home country. The application is excluded from the federal territory.
You also do not meet the requirements of section 16a (4) AufenhG, according to which you could be granted a residence permit to search for a training place.
If I understood, you have applied for residence permit after paragraph 16a (1). But this residence permit can be issued, if your son would start a vocational training, to job as a specialist or to work if he has a diplom about a completed vocational training. But if he would like to get another employment, he need a Visa, which were applied in the home country.
He also does not fulfill the requirements of the paragraph 16a (4). According to this law he could get 6 month in order to give the foreigner the opportunity to look for another training place (Ausbildungsplatz.)
I hope that this answer can help you. If you need more advice, you can contact me through the mbeon application. You can download it free charge. You can do this using one of the following links:
The app and the messaging are confidential.
You can find me in the app under the name: Alzey, Herr Zsigó.
Thank you for your trust.