Well ... if you fulfill the normal requirements, independent of your nationality etc., why not?
There is probably no law paragraph for your specific situation, so I can't quote it ... but basically, if you legally worked and paid the insurance, you should be able to get something out of it too.
The most important conditions are
- 360 or more days employed in the last five years
- 360 or more days employed since the last time you got ALG (if ever)
- Unemployed (of course)
- Telling the Arbeitsagentur than you're unemployed as soon as possible
- You are actively searching for a new job, and if the Arbeitsagentur knows some reasonable job for you, you don't refuse. (If you do, because you don't think it's reasonable or whatever, it's not completely gone; there are temporary bans too)
- A acceptable end ob your old job: reason, notice periods, etc. (A "I hit my boss on the nose and then never came back and ignored the phone" is proven to be bad :p Also, with a "everything was alright, but there was a job with more money, and I quit before getting accepted" you could have a hard time convincing them)
and other points in the navigation to the left.
As for your Aufenthaltsgenehmigung, it shouldn't affect anything as long it doesn't expire. If, at this point, you have no job and already used up the ALG, ie. you get "Hartz4", that could be a bad.