I just replaced my car battery a week ago, and my car shut off on me yesterday, what is the problem?

I just replaced my car battery a week ago, and my car shut off on me yesterday, what is the problem? - 1
Added (1). I drive a 2006 Ford Mustang GT, and a little over a week ago my car was having problems with the battery. It first happened when I was driving one night then my radio shut off, then my headlights proceeded to shut off along with my dash lights. Then you could hear stuttering in my engine and the exhaust. I turned off my car and tried to turn it back on and my engine stuttered for about 1-2 seconds followed by a bunch of rapid clicks. Replaced the battery and it happened again a week later.
Added (2). I replaced the battery a week ago and it was running fine then it did all what I had previously mentioned when it was messing up before. My radio and dash lights turned off, then my headlights turned off. My traction control and my ABS light came on, then my engine started to stutter then finally shut off. Even with a new battery.

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