You have no possibility to get BAföG (state interest-free credit for students withou financial means). For asylum seekers it is only possible if they lived and worked in Germany for at least 5 years before or their parents lived and worked for some years.
You can study using normal financing for asylum seekers. After first 18 months of the asylum procedure, if you study but still don`t have a final decision, it is possible that this money will be paid as a loan or it can be just granted to you. As a student in Germany you normally are allowed to work for max. 20 hours a week, although, I beleive, as an asylum seeker you additionally need a special permission for each kind of occupation, for a student job too. I would check it anyway.
It is important to make contact to a consulting office of a foreigners` department, especially in the university you want to study at. Some universities have special consulting for asylum seekers and refugees. Ask there for consulting in financial questions.
An educational consulting, which is recommended by BAMF, is here: https://***.bildungsberatung-gfh.de/
There are also many kinds of stipendium, inform yourself in Internet or in a councelling center.