If not the alternator what could it be

Ok driving down three days ago the radio starts
blinking on and off the ABS light and the traction
control light comes on my car dies. Jumped it off
made it a couple more miles down the road ABS light
comes on traction control light comes on car dies.
So get the car home my son says take the battery to
have it tested took it two different places to have it
tested Dad cell got a new battery put it in, all the
while thinking it's an alternator issue, but my son
checked the voltage and everything on alternator it's
fine. So I have the new battery in drive the car 25-30
miles no issue. that was during the day didn't have
headlights or heat or radio or nothing running on it.
Coming home that night lo and behold ABS light
traction control light comes on car dies I coast into a
parking lot wait about 10 minutes Crank It up and I'm
able to get it parked. It was late it was dark full with it
in the morning come back the next morning pick the
car up thinking I'm really going to have to have it
towed car cranks right up drive it home that's another
20 mi no problem. I don't get where the problem
could be all the voltage coming off of alternator and
the battery of course it's brand new battery are great.
The only lights coming on are the ABS and the
traction control light when this happens the battery
light's not coming on or staying on nothing like that.
and like I said it done fine both times I've driven it
during the day with no headlights no radio going
nothing it's done fine. Could that still be the
alternator or what else should I check.