In Daniel Cassidy’s insane work of etymological fiction, How The Irish Invented Slang, the phoney professor of Irish Studies claimed that the word kitty, meaning a pot of money in a gambling game, derives from the Irish phrase cuid oíche. This is highly improbable.
The origins of the word kitty are unknown, though there are several possibilities. You can find some information at these links:
The phrase cuid oíche (earlier spelling cuid oidhche) is an historical term. It literally means ‘a night’s portion’ and it refers to the entertainment which a lord could expect from his subjects. It is pronounced roughly as cudge-eeha and has been anglicised as cuddy. In other words, it is not a good match for kitty in terms of pronunciation or of meaning.