The possessive singular of all English nouns is formed by adding -'s: Alexis's. If Alexis's seems awkward to you, you may use the Frenchified possessive "of Alexis," but never use the plural possessive form, which is to add an apostrophe after the final -s of the plural, for a singular noun.
Use whichever form you use to say it Alexis' or Alexis's. Use the form the way you pronounce it.
The singular possessive form is week's.
The singular possessive form is classmate's.
The possessive form is Amos's.
The singular possessive form for the noun gypsy is gypsy's.
The singular possessive form for country is county's.
The singular form for the plural noun countries is country; the singular possessive form is country's.
singular possessive: boy'splural possessive: boys'
The singular possessive form is speculum's.
The singular possessive form is aircraft's.
The singular possessive form is frontiersman's.
The singular possessive form is contralto's.