Thank you for sharing your situation with the Wefugee Community!
Unfortunately, I am not familiar with the Italian residence law. But if you are holding a residence permit in Germany, for example, and you have a valid travel document, you are in general allowed to travel abroad. However, it is not clear to me, which document you are actually holding. Maybe you can try to explain a bit more in detail. This would help in making any research regarding your question.
All the best,