How can i stabilize the backsprocket?

I wonder if your rear sprocket is sitting flush on the hub. It's common to have to file the center hole a bit to fit the sprocket flush, I had to do this on mine. If the sprocket is balanced on that little hump of the hub then it will be able to shift around and go out of alignment.

Another possibility is the rag joint bolts are coming loose. That can be fixed with blue threadlocker.

And check the spokes for proper tension. Perhaps they are settling in if this is a new build.

A photo of your set up might help diagnose the issue.

I recommend getting a sprocket adapter, it's much easier with less maintenance.