Bad alternator and or battery
either that voltage regulator inside alternator (IC REGULATOR) is no good or you have serious ground issues somewhere.
Anything above 13.5 volts or so is charging a little with 14.2 to 14.8 being optimum.
Ohms law; it takes a volt to push an amp across an ohms resistance. in other words if charging voltage isn't greater than battery voltage it won't charge. voltage must exceed substantially to charge substantially.
Just because a battery reads 12 volts with no load, it doesn't mean it's any good. If it hasn't got enough power to run your radio, it's had it. How old is it? Assuming your starter motor draws about 200 amps,a good fully charged battery should hold at around 9 volts under a load.
replace it
Alternator is brand new, battery tested good, yet my battery isnt charging, I have voltage reader built in my car so i can tell how much voltage goes thru my car it jumps between 9.5 to 14.1 its good between 12.6 and 13.0 when nothings on accept radio but when i turn on my radio lights windshield wiper and blinkers voltage drops big time what do i do how do i fix it and how much will it cost to fix it btw its a 96 sentra