Can a employer deduct from your hourly wage every time you are late for work?

My Hourly wage used to be Twenty dollars a hour, now it's Twelve dollars and forty cents. I work a split shift six days a week, so I basically go to work twelve times a week. Now my employer has always joked around with everyone saying things like if you make that mistake again I'm gonna take a dollar off your pay, but he never ever did so. When he told me he was gonna take ten cents of my hourly pay I thought it was another one of his jokes, until he handed me a contract to sign to give them permission to do so, which I did not sign and never heard back from him about the matter. the contract was signed by his Daughter who is also a owner I think, she does payroll and is human resources. I kinda forgot about the matter cause they never said anything to me about not signing the contract, but then I happened to look at my pay stub and noticed my pay was around $18 a hour. I've never heard of anything lie this before, do they have the right to do this? It's getting to point where I cant afford to go to work now.