I have no idea where it came from, but that word is standard on all no trespassing signs in the US.

PROBABLY what happened is some law got written saying that "no trespassing signs must be Posted at least every 50 feet around the perimeter so they're visible" and magical thinking lawyers latched on to that word "posted" and started to convince themselves that it was a magic word which must be used in order to make the difference between a "please keep out if you want" sign and an official "the property owner does not authorize you to enter" sign.

And so now every goddamn sign has that word in some conspicuous and language incorrect way.