No, apostrophes should not go after the period.
In English punctuation, the period (.) is used to indicate the end of a sentence. Placing an apostrophe after a period would be incorrect as it would create confusion about the intended structure of the sentence. Apostrophes are used for contractions (like ‘it’s’ for ‘it is’) and possessives (like ‘John’s book’). After a period, the sentence is complete, and any subsequent words should start a new sentence or idea without any punctuation marks directly following the period.