taxes

Ok so I told my ex I was going to claim my son on my taxes so I could get a new car (my cars on its last legs) and he said it was fine but now he's saying he's going to claim him which has me very aggravated bc I was counting on that money since I only work part time and won't be getting much back by myself on taxes. my question is my son only goes to his dads 2 days each week (not all the time tho) and he doesnt pay child support and has never even asked if I needed help with diapers or anything else for our son and won't even watch our son on days I work long shifts so my mom doesn't have to (always says he's made plans or has a date) but from what I know a child must live with the parent 6 months out of the year.. can he still claim him? (also he has a new vehicle and makes about $2000 every other week so I honestly don't know why he would need the income tax money)..

fyi I'm in Florida