thank you for sharing your question with the wefugees community.
If a couple (married or unmarried) stays together with a mutual child, Jobcenter presumes a "Bedarfsgemeinschaft" (can be translated as community of dependence). That means that everybody is expected to stand in for everybody elses needs in the Bedarfsgemeinschaft. Normally, also Sozialamt (Asylbewerberleistungen) is doing the same, so you can be lucky that it didn't happen in the past with you and your boyfriend.
Jobcenter will now callculate all the income of you, your boyfriend and your children (his income + maybe your Elterngeld + Kindergeld + maybe Unterhaltsvorschuss for the other child) and calculates if that is enough for the 4 of you to survive. For jobcenter it doesn't matter if your boyfriend has additional bills to pay.
Your best chance to be assesd seperatly from your boyfried will be to find your own place...
I hope my answers were helpful and I would be very happy if you would contact me again with further questions. I'm a consultant with mbeon and I‘ll be glad to help you over a longer period of time. Mbeon is an online advice for migrants via the mbeon app, which you can install on your smartphone for free. Download it from App Store or Google Play Store. You can find me in the mbeon app and get confidential individual advice in a secure virtual space without other people reading our conversation. Further information: www.mbeon.de.