Welcome to the Wefugees Community and thank you for reaching out to us.
As father of a German child, you are probably holding the residence permit according to section 28 of the German Residence Act, right?
Whether the residence permit will get extended or not, is not necessarily dependent on the fact that you are (not) living together in one household. Please read my answer in this thread for more information.
In any case, please also don't hesitate to get back to us with any further questions.
All the best for 2022,