With your residence permit (I presume it is according to paragraph 28 of the residency law, it should be written on the front of your residency card), you are entitled to support from Jobcenter. You need to make an application for unemployment benefit (Arbeitslosengeld II). Please note that they will take your financial needs and ability to pay for these by yourself as a family into account. This means they will **** at any income your girlfriend has to see if that can cover some of your expenses. They will calculate the Kindergeld you presumably receive when calculating how much money to give for your child.
The Jobcenter can provide you with money each month for basic living expenses and to help cover the rent. If you are in receipt of money from Jobcenter, you can do the German language ‘Integration course’ free of charge. Here is more about the course:
They can also pay for things like the costs of applying for jobs. They can also finance you to do other types of training courses once you have improved your German.
If your girlfriend has enough income which means you are not entitled to Jobcenter support, you could apply for another rent benefit (Wohngeld) and additional child benefit (Kinderzuschlag). But I recommend first applying with the Jobcenter.