68 Barracuda Formula S 340 car Charging

I’m not getting 12 V out of the field tab on the alternator, I’m getting 0 and only getting 11.4 on the larger post on the alternator. I’m getting 12.3 volts at the battery.
The Field connection from the regulator will only have system voltage when the regulator is sensing very low voltage.
Steady zero volts when the engine is running shows the regulator is not allowing electricity to the field connection. (how it works shown here in post 5)
Next check is what voltage the regulator is seeing. Do this by measuring voltage at the input connection, labeled 'ignition'. The next nearest location to check with with a probe is the connection at the ballast resistor.

11.4 V on the larger alternator post.

That is the output terminal of the alternator. It should be almost the same voltage as the battery positive terminal under all conditions.
Engine off, lights off, it should exactly the same voltage.

12.3 Volts engine off is a low battery.
11.4 V engine running confirms a batttery with low charge.
Charge that battery with a charger. Do not use the alternator to charge it if at all possible.

Here’s a pic. Any idea where I could find a correct alternator quickly ?

View attachment 1715729587

That alternator should work.
If both brushes are insulated and have tab terminals, ground one of them.
Example shown in post 3 of this thread Identifying Chrysler Alternators (1960-1976)

Based on the information so far the most likely issue is no current is flowing into the rotor.
Therefore see if there is voltage on the input side of the regulator with the key in run.
If yes, then check the regulator. Points type regulator is easy to diagnose visually.

After the battery has been recharged using a charger, it would be OK to test the alternator vs regulator using a temporary jumper to power the field.
Do this after the engine is running on slow idle and do not rev the engine.
Because the voltage is not regulated, it will increase with rpm. Any and all electrical devices, including the battery, will draw more current with rising voltage. This can and will cause damage. The ammeter will show how much current the battery is drawing. So that is one way to monitor the danger. If you see the alternator is now working, great. Shut it down and fix the regulator.