Hi @maribel999
If your asylum application is rejected, you can continue the Ausbildung with Ausbildungsduldung/16g. When you have completed it, you would usually change to the permit 19d. 19d is for people with a Duldung and a qualification and is importantly ‘for the purpose of employment’ (zum Zweck der Beschäftigung). You can only get 19d if at least your principal reason for staying in Germany is for employment.
I’m not an expert on the area of Duales Studium but from what I have read there are different types. One is a study programme with integrated Ausbildung and the other is a study programme with integrated work experience. In my view, in either case you are primarily a student, even if you are working as part of it. The name of it is Duales Studium, i.e. first and foremost are the studies, rather than it being called Duale Arbeit or such. If someone from abroad wishes to come to Germany to do a Duales Studium, they have to apply for a visa for study purposes and not for work. You can see this in a detailed brochure here in German and English produced by the state of Saxony:
https://***.zuwanderung.sachsen.de/download/SMI_Zuwanderung_Infoblatt_Duales_Studium.pdf
The only alternative I see is to study part-time. i.e. you work in the area your qualified in and earn enough to get 19d, and in your free time are free to do further studies or qualifications.
Best,
Éanna