Will an alternator stop your car from starting?

while i was driving my car shuts off at nite while the lights are on, and i got it started back up and shuts off and comes back on

If you have a bad alternator it can cause starting problems. More likely because you were driving and not charging the battery, while draining it. The alternator re-charges while you drive. When you turned it off & came back the next day there was not enough juice.