I can give you an answer based on Florida law as I am a practicing attorney in the State of Florida in the United States.
Here, the payment of child support is separate from the right to visitation. Whether or not the parent requesting visitation has paid child support, they are entitled to visit with the child.
Also, regardless of how much time has gone by since the last visit, the parent does have the right to visit the child.
You are not obliged to permit him to see the child. Also, the child is older now and, if she does not want to see her father, does not need to be forced to.
The father is always free to take the matter to court. However, this will cost him time and money which is typically a deterrent (especially for a father who has not seen his child in the last 3 and a half years. He also may not want to take it to court because then the lack of child support issues will also be introduced.
In summation, you are not forced to allow the visit, but you do run the risk that the father will take you to court over not allowing him to see his child (although this seems unlikely here given the totality of the circumstances).