Well high voltage can only come from alternator, new or not.
Voltage regulator IN the alternator sets the output voltage, nothing else.
Engine size can matter for wiring, what engine do you have?
Battery is grounded to engine, usually on or near starter motor bolts.
This is the ground for starter motor and alternator, sensors and cab
Often there is a smaller ground wire from battery terminal to Rad support, this is the head light ground.
From the back of the head on the engine there will be a ground strap to the firewall, that is the main cab ground.
There is often a ground strap on or near one of the motor mounts, from engine to frame, this is the ground for tail lights and often the fuel pump and fuel gauge.
I would test alternator wiring.
Key off
Set volt meter to DC Volts
Put black meter probe on Battery Ground, red on battery +
New battery will show 12.7 or higher volts, remember what it shows, that will be "battery volts" in the following tests.
On the back of the alternator is the B+ terminal, has a nut to hold the wire.
Red probe on that terminal and black probe on alternators case, any ground is fine.
You should see "battery voltage"
Unplug the 3 wire connector, 2 wire on some engines, the Yellow wire should also show Battery Voltage.
If B+ or yellow wire doesn't show full battery voltage then you have a blown fuse or fusible link.
Now turn on the key, engine off
Test Light Green wire on the connector should show battery voltage, if not then blown fuse in cab fuse box.
If there is a short White wire on 3 wire connector, make sure it is not frayed or loose and is plugged in to the single plug next to 3 wire plug in.
Google: car battery measuring amp draw
That will give you ideas on how to track down a battery drain
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