Welcome to the Wefugees Community and thank you for sharing your situation with us.
In order to be able to give you tailored information and advice, we would need some more details about your and your family's circumstances. Is your marriage recognised/registered in Germany? Which type of residence permit are your wife and child holding? And which nationalitites? Are you officially registered as father of your child (named in the birth certificate)?
In general, a family reunification with a German citizen is definitely easier than with a non-German person living in Germany. If certain requirements are fulfilled, it is nevertheless also possible to obtain a visa based on family reasons in the latter case. In this regard, it may also play a role if your wife is having a (sufficient) income to cover the family's costs of living, for instance. The authorities could also ask you to prove basic German language skills.
Depending on your conditions, you may also consider to apply for a residence permit to take care of your child (Aufenthaltserlaubnis zur Personensorge). We discussed this type of residence permit already a few times on this platform. Please see this thread accordingly or have a look at the information provided here. For the "Aufenthaltserlaubnis zur Personensorge" it will be essential though that you are officially registered as the father of the child and you share the custody as well. Please be aware that the issuing of this residence permit is at the discretion of the immigration office (no legal right) and it will be better to involve a lawyer here.
In general, I would highly recommend you to contact a migration counselling office in the first place. There are numerous offices all over Germany and they offer free of charge and confidential advice. Please let us know if you need help with finding a respective organisation close to your current location.
I hope this helps and don't hesitate to get back to us if you want to discuss your case further or you have any other questions.
All the best,