Yod, like most other letters, can only get a dot in it called a "dagesh chazak." This indicates that the affected consonant should be geminated, or doubled the way you would double, e.g. the 'b' sound in "subbasement."
So, for the word in your example, שִיֵּץ, you would say "shiy-yatz" rather than "shiyatz," and your name would be pronounced "Chay-ya" rather than "Chaya."
Congratulations on your intention and efforts toward pronouncing prayers correctly! If you can incorporate this detail of correct pronunciation into your habits, you'll be taking a big step toward exceptionally precise pronunciation