“Should of” does not mean anything. Neither does “could of”, “must of”, “would of”, etc.
The reason you’re saying it or writing it like this is probably because they are contractions – “should’ve” (should have) and “could’ve” (could have) – which makes it sound like they have “of” in there somewhere.
“I should have/should’ve gone to the party” is correct. “I should of gone to the party” makes no sense.
This is why making assumptions is a bad idea. Lazy writing and lazy speaking can leave some negative impressions on all the right people. So, know what you’re saying before you say it. If you’re ever in doubt, it takes just a few seconds to check!
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