Dear Smart Djaba,
Welcome back to the Wefugees Community and thank you for reaching out to us again.
"Handbook Germany" are explaing details on "how to travel as a foreigner/refugee in Germany" quite well on their website (also in various languages). Let me quote their explanations:
In principle, you can travel abroad if you hold a travel document for foreigners or stateless persons (the so-called "Gray passport"). For most countries, however, you need a visa, plus, not all countries recognise the "Grey Passport" as a valid travel document. Before planning a trip, you should contact the embassy of the country in question to see whether they recognise your travel document and issue you a visa or not. On the last page of this UNHCR report, you can see a list of countries which recognise the "Gray Passport". Whether you will be issued a visa depends on various factors such as your country of origin, nationality, your situation in Germany and alike, so it is difficult to predict the result of your visa application.
As someone who holds a "Grey Passport", you can go to all the Schengen States without a visa and stay there for up to three months. You can find a list of Schengen states at auswaertiges-amt.de.
Please note: You could lose your residence permit in Germany if you travel to your home country while residing in Germany under subsidiary protection or due to a national ban on deportation. If the Immigration Office learns about your trip, they can initiate a revocation procedure, and you could lose your protection and right of residence in Germany.
And yes, if you are receiving an allowance by the jobcenter, you need a permission before travel. You may not exceed 3 weeks absence per year.
I hope this helps and please don't hesitate to get back to us with any further questions.
All the best,
Meike