The gun's upper frame at least is military, not commercial. So far, based on your description, you have a Mauser gun, (byf) made sometime in 1941, (the 44 ending of your serial number is NOT the date of manufacture. The 41 on the upper receiver behind the barrel is the date of manufacture). It has a Crown over N nitro proofed commercial barrel, which would be a replacement and a magazine numbered in the police style.
The 41 date would make it too late for a Weimar police conversion, but It may be an East German reissue, (that "X" under the barrel might indicate this). Does it have plastic grips?
As David pointed out, we really need photos to help you further.
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