What could be causing my car to have a charging problem? Its a 03 dodge stratus

This definitely sounds like an alternator. Try charging the battery fully. Run the car without any assistance from jumper cables hooked to another car. Use a simple volt meter on the battery to see what kind of voltage its getting. Should be 13.5-14.2ish. I know you have a new alternator but this seems like a charging issue. A shop will have a load tester and can dig a little deeper. Alex

Quite possibly a PCM related issue .. The alternator voltage regulator is an integral part of the PCM (Power Control Module) .. Professional scanner can 'full field' the alternator bypassing the regulator for accurate testing .. This needs to be done by qualified personnel .. Parts stores don't qualify! ▪️https://repairpal.com/repair-shops▪️