thank you for sharing your question with the Wefugees Community!
I found a thread here on the Wefugees Website where a similar question was asked. There you can find all the prerequisites for a resident permit through a German familiy member. Don´t be confused, the information quoted is from the Berlin Senate - if you are from another city the information still applies, you just have to replace the information regarding "Berlin" with the city you are living in right now. Please also note that you don´t need to show proof of German language skills - that doesn´t apply on your case.
If you fulfill all the prerequisites it is likely that you receive a resident permit. Please also keep in mind that it is important that you not only have the "formal" paternity (Vaterschaft) but that you take actual care of your child that requires you to stay in Germany, for example regular visits etc. This is of course easier to proof if you live together with your child.
If you are not sure if you fulfill all the prerequisites or if your application gets rejected it might be helpful to contact a lawyer or if you can´t afford one a counselling centre/office. I will link a website for you where you can find independant and free counselling close to you: https://adressen.asyl.net/language/en/welcome-to-informationnetwork-asylum-and-migration/
I hope this answer was helpful. Please don´t hesitate getting back to the community if you have more questions.
All the best
Note: Please keep in mind that we can´t provide qualified legal advice via the internet and that any information given can´t replace such legal advice.