Dear @Maxtin,
Welcome to the Wefugees Community and thank you for reaching out to us.
I assume we are talking about an asylum seeker whose asylum decision is still pending and who holds a so-called "Aufenthaltsgestattung"? Handbook Germany is providing very helpful information (in various languages) on the rights of an asylum seeker (with Aufenthaltsgestattung) in general including studying (in short: you are allowed to study and it doesn't have an effect on your asylum case) and working. They explain here:
If you have an “Aufenthaltsgestattung”, i.e. a proof of arrival ("Ankunftsnachweis") or a "Duldung", your access to the labour market will remain limited. Self-employment is in principle not allowed and to work as an employee, you must first apply for a work permit at your immigration office ("Ausländerbehörde").
Asylum seekers can obtain a work permit if they have been in Germany for 3 months and are no longer obliged to live in an initial reception facility. If you still have to live in an initial reception centre, in case you have underage children, you can obtain a work permit after 6 months- and if you don't have children, after 9 months. Rejected asylum seekers whose application have been rejected due to Dublin Agreement, i.e. other EU countries are responsible for their case AND those who come from a safe country of origin and have applied for asylum after August 31, 2015, cannot obtain work permits.
IMPORTANT: Your work permit will be only valid for a specific job. Your future boss will need to fill a form to describe the offered position, and you should apply for a work permit. Once both forms have been filled and submitted, the immigration office is obliged to react within two weeks. If you have not received any answer, contact a counselling centre. You can also submit an emergency application to the Administrative Court.
Under very specific circumstances it can make sense to withdraw the asylum application in order to apply for another residence permit (for i.e. working/training/studying). But this should be carefully discussed with a lawyer!
I hope this helps and in any case please don't hesitate to get back to us with any further questions.
All the best,
Meike