I have a 2003 hyundai sonata

I have just replaced the battery yesterday and last night I drove my son home and the car just slowly powered all lights off and suddenly I had no power at all... I let the car sit for a few minutes and then restarted the car and it ran for another 500 feet until it did it again... I am wondering... before I jump to conclusions and say it is the alternator, I there something else that COULD be the culprit that I can personally check within reason myself on the vehicle that might be just as simple as a fuse or am I being too optimistic her... Please help me... Stuck Monkey!

. Remove and fully charge the battery. Even before installing a new battery, they should be charged for approximately 3 hours, using a 6-amp. Charger. Most auto parts stores will do this for free.

. Clean the battery terminals and cable connections with abrasive cloth. Afterwards, apply dielectric grease.

. Check the regulated battery voltage. It should be 14 to 15 volts, with the engine running. Simply connect a multimeter across the battery terminals--red to red and black to black. If it's low, the voltage regulator/brush assembly likely needs replacing. For most people, it's easier to install a new alternator. I would also clean both ends of the cable, going between the alternator and the battery, with abrasive cloth. Alternators are battery maintainers, not chargers.