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The most common (and legally clearest) type of rental contract in Germany is unlimited with termination notice periods stipulated by law (which, in your case, would be three months).
Time-limited contracts are difficult to enforce - the contract must tell the reason for the limitation, and it can only be one from a very limited list of reasons defined by law. Many time-limited contracts are invalid - and then default to the abovementioned more common type. Therefore, it is advisable to have your contract checked by an expert (either a lawyer, or a tenants' association "Mieterverein", which you would first have to become member of).
If the limitation in your contract is indeed valid, you have to either pay the rent until the contract ends or find a mutually agreeable solution with the landlord. It will cost you in both cases!

In addition to what Beppi mentioned, there is something called the 鈥淰erbraucherzentrale鈥� in every sizable city. I am posting a link below to the website of the one in Dresden (German only). It is a kind of consumer protection agency. They give advice about things like warranties or guarantees for things, contracts, problems with the telephone or internet service etc. Sometimes they can give good advice or pressure companies to deal with one fairly. Other times they will not succeed and recommend you take a lawyer if it might really be worth it. They usually start off with a pretty reasonable fee up front. The thing is that if one has a determined opponent that will fight things all the way to a court case, then it usually takes a year or 2 or 3 and can be very expensive both for lawyers and court costs if one loses.聽 Even when one is in the right, an actual lawsuit for such things is either too time consuming or not worth it from a risk/benefit analysis.