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Before I try to answer your question, here are a few things to keep in mind:
As a refugee you are allowed to travel within EU, but you can only stay abroad without a visa for a maximum of 90 days within half a year. So if you want to study in Germany you need a visa for that. Here you will find extensive information about this topic in English:
In addition you will have to apply for a residence permit at Ausländerbehörde once you came to Germany.
I don't know if the procedure outlined above is applicable for refugees. So first of all I recommend you to get in contact with the Italian aliens department to figure out if it is possible for you to study abroad in general. After that you should get in touch with a German agency abroad (like an embassy) to get detailed information about the next steps that you have to take.
Now to come back to your initial question: I would say it always depends on the terms and conditions of the scholarship that you want to apply for (e.g. if they are open to foreigners etc.). Do you have a specific scholarship in mind that we can do some research about?