screen -r spawning new prosses

C-a z suspends your screen process. If your shell is bash, you can see the stopped process by running jobs and resume it with fg. Detaching is a different concept.

To detach from a session, use C-a d. You will still see the screen process in your process list, and you can list it by running screen -ls. Resume with screen -r, but read the man page about the different ways to resume a running screen session.

Congratulations on learning about screen! It's an amazing tool.

Try to detach within a screen:

ctrl a d

to reattach:

screen -rd (detaches the screen first if was attached)

There is also:

screen -x (attaches the screen again, so you can watch the screen with two sessions)