My Ex Husband is living in a home that I bought about 6 year ago. I pay the mortgage and all repairs on the house. Does he have any claim to the property?

If the home is in your name only, then no, he has no claim. You used the word "squater" in the title of your post - if you're asking is there any such thing as "squatter's rights" the answer is no. You can have him evicted, but you need to be sure to follow the legal process for eviction in FL. Post back if you need more details on that.