With the engine off, put a low wattage 12V bulb (interior, side repeater,
stop/tail or similar between the +VE battery post and its clamp. If the
bulb glows pull fuses until it goes out. Then you will be able to
determine the offending circuit. Could be the alarm system.
If it glows but doesn't go out, get the alternator checked out, or if
mecanaical lift its heavy duty connection, then if separate its control
connector that feeds the voltage regulator.
Do not attempt to start or run the engine with the lamp in series,
but in any case the engine won't start with the lamp in series.
An engine running with no battery connected will expensively fry
the electrics.
This should be your first, cheap and easy, start on diagnosing
the problem.
If the above fails, we get on to has the problem always been there,
when did it first occur etc?
Also to progress further you would a meter to measure any
drain on the battery, I'm surprised this wasn't done when you
had the battery checked.