Dear @Yoseph_Mostafa,
Welcome to the Wefugees Community and thank you for reaching out to us.
It was not clear to me from your explanation why your residence permit (I assume you are holding one according to §16b) can not be extended. This would most probably be the best option. Since you are working, you shouldn't have issues to secure your livelihood (which would be one requirement for the extension). In case there is no other option than applying for asylum, you can of course do so. You have a Somali citizenship, right? I am not a lawyer and I can't make an assessment as to how the Ethiopian papers (travel documents) might affect your chances of recognition as a refugee.
Regarding the asylum application as a student, my colleague answered a very similar question here. He stated: "As long as [someone] still has a valid residence permit and applies for asylum before it expires, then they are not obliged to live in a special refugee reception centre. For people who have residence permits and apply for asylum, the rules around accommodation are different to a person who does not have a residence permit. However, if they apply for asylum and are not able to pay for their own housing, then they will be housed by the social office (Sozialamt). This would likely mean the person would be housed in a refugee centre (Gemeinschaftsunterkunft)." However, I am not sure whether this only applies as long as the current residence permit is valid for at least 6 months. I would therefore recommend that you seek advice from a lawyer or an experienced counselling office (i.e. "Asylverfahrensberatung") as soon as possible.
I can't make any statements regarding your scholarship because I don't know the individual conditions.
I hope this helps and please don't hesitate to get back to us with any further questions.
All the best,
Meike