I have seen some people write "my wife and self were invited" Or "Please give access to Tom and self"
Is this is correct way of using "self" in a sentence? Or there is a different way?
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That is not idiomatic English but it isn't strictly incorrect. It would mark the speaker/writer as a likely ESL person, as it sounds slightly awkward to English/American ears.
Almost universally, you would say "my wife and I were invited" and "please give access to Tom and me". Note that the self pronoun goes last (eg, "Tom, Mary, and I were invited").
As others have said, your usage may be more common in certain dialects of English. I'm answering from the perspective of a North American native speaker of English.