Engine randomly shuts off while driving

When I drive my vehicle it will randomly shut off when I'm driving. Both of my turn signals will turn on right before my vehicle shuts off. Once it shuts off the battery will not turn on. Headlights still work, all power still works. The odd part is when I turn my headlights off then back on the car will start back up but will experience the issue again. Once started both turn signals will be on. I had the battery tested original and it needed to be replaced. I bought a brand new battery, but later that day it happened again. I even started the car and disconnected the battery and the car was still running to check the alternator. I'm in a big stump on this one.