Several possibilities; faulty battery, faulty or corroded cables / connections, faulty alternator, faulty alternator wiring, loose / worn alternator or accessory drive belt, worn / faulty drive belt tensioner.
First step - have the battery and charging system tested; including the alternator - for free - at any local auto parts stores in your area. Next, make sure the battery connections / cables and terminals are OK - clean and tight; with no corrosion build-up - at both ends of each of the positive and negative (ground) cables to and from the battery.
When the battery and charging system - along with the alternator is tested - be sure to obtain a written, detailed test report; containing the voltage, amperage and test conditions, plus the test results.
With the car off, all lights off hook the meter probes one to the + terminal of the battery and one to the + wire/cable that you removed.
You must start with a known full charge battery tested after a full charge with a battery hydrometer to test the electrolyte in each cell at 1.25 or higher S.G. (specific gravity). If battery is maintenance-free cut off the 3 cell cover and inspect the electrolyte charge and level.
With the battery test and known good, hook up in the car with clean terminals, no grease. A helper may be needed.
With a cold engine, and with a voltmeter at 20 VDC, read the meter as the motor is started. Read the meter as the motor fast idles, read the meter as the idle comes down to normal and finally read the meter as the RPM is upped to 2500.
After recharging the battery and testing with an hydrometer must have 12.7 V
No hydrometer get one, battery terminal voltage at least 12.7 VDC
While starting cold motor and battery hooked up, during starting or cranking no less than 10 VDC.
At cold higher idle at least 13V to 13.5V
At warm engine 750 idle at around 13.25
At 2500 RPM at full voltage of 15 VDC
If all is good, shut the engine off.
With a good multimeter set to 10 A maximum for Amps and test leads correctly placed on meter, with one lead as common and one lead at the amps 10A whole. Remove the + lead from the battery with all the wires/cables. Clean the battery + terminal and the + lead that you disconnected.