Welcome to the Wefugees Community and thank you for reaching out to us.
I am not sure, if I fully understand your situation and question though. Is it correct that you received a Schengen visa from an EU country in its embassy in Ethiopia and now you would like to know if you can apply for asylum in the EU?
First of all, if you apply for asylum in one of the EU countries or signatories of the so-called Dublin regulation, you will most probably be asked to go through the asylum procedure and stay in the respective country which issued the visa in the first place. Regarding the general topic of applying for asylum with a Schengen visa, you may want to read the content of this thread, in which we discussed a very similar question before.
In any case, please don't hesitate to get back to us if I did not understand your request correctly or if you have any further questions.
All the best,