Tse miy kit is translated to This is my cat... I typed that in and it said that it was incorrect but the correct translation was It is my cat... In this case, that is wrong because Tse means this not it is in this phrase.
Мій-matches with masculine nouns Мій кіт Моя-matches with feminine nouns Моя кішка
Both mean "my," but possessive modifiers as well as adjectives will have to match with the gender and number of the noun in all cases.
Many other languages (German, French, Spanish) have both masculine and feminine words for ‘cat’. Clearly this one is masculine, but is there a feminine one to go with it?