The man I believe to be the father of my baby loves him and wants to raise him, but my ex boyfriend is wanting to cause drama and says he wants a paternity test on the baby. Can we stop him from getting a paternity test since we are the baby's legal parents?

This will depend completely on where you live, in a few US states I understand that if you are married and a father is listed on the birth certificate, antoher perosn can not be forced to take a DNA test and another man does not have legal standing to ask for a DNA test.

But in most areas yes, he can force a test if he believes he is the father.
And if there is a chance he is the father he has the right to know, esp if he wants to be part of the babies life.

If you are honest with yourself - is there a chance that he could be the father? Any chance at all?
If there is, no amount of hoping and wishing is going to make this go away.
If he is a dad, he has a right to know.
I know you probably want to stop this because you are afraid of the outcome, but if he truly believes he is the dad - he may not leave you alone until he knows the truth.

Are you married to this man whom you believe to be the child's father? Is his name on the birth certificate? Your ex boyfriend wants to know the truth - you call that drama but he calls it finding out the truth. Are you afraid here of finding out the truth?