Can my parents claim my 3 year on their taxes when I have split custody with his father and its my year to claim my on?

I am 28 years old and living with my parents. They can't claim me I know on their taxes because I made more than 4500 last year. But they are saying that they can claim my 3 year old son because they can show that they provide more than 50% of the care for him. I.E just food and housing. I paid for his diapers and medical expenses. My question is can they actually claim him even though I have split custody with the child's father. Meaning we alternate years on who claims him on their taxes and this is my year to claim him.