could of / would of / should of
It has always been “have.” You are transcribing a contraction you misheard.
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Wrong: I could of told you.
Right: I could have told you.
Could’ve is the contraction. Spoken fast, it sounds like of.
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Wrong: We should of tested it.
Right: We should have tested it.
Same. Should’ve.
Where it comes from
Say could’ve out loud. It sounds essentially identical to could of, and if you’ve mostly heard the phrase rather than read it, of is a completely reasonable guess at the spelling.
It’s still wrong. Of is a preposition and cannot follow a modal verb. There’s nothing for it to do in that sentence.
The fix
Expand the contraction. Could’ve becomes could have. If writing of there felt fine, that’s the habit talking—the phrase has no of in it and never has.
Now go expand every contraction you own.