Welcome back to the Wefugees Community and thank you for reaching out to us.
First of all, as long as your asylum procedure is still pending, you can not be deported. So don't worry about that!
If you want to move to another place as asylum seeker, you need to submit a so-called "Umverteilungsantrag" at the immigration office in the respective "new" municipality. Please be aware that the procedure is not easy and you may want to contact a migration counselling office to get support - especially in drafting and formulating your good reasons for moving and justify the application. Did you officially recognize the paternity already and do you share the custody for the child?
I think this would be a precondition for a successful process.
I hope this helps and all the best,