Do I have the right as a mother to keep my 21 month old son from his dad if he is vindictive trying to take..?

him from me. This guy has had little to no interest in our son since he was born. He was ordered to pay child support and since then he has filed false CPS allegations against me just to try to deem me unfit but has failed every time. He even makes little comments like I will get my son from u , I am not gonna pay u any more child support and I am gonna take my son back home (Jamaica) to stay. SHould I keep my son from him and only allow supervised visits???I am fearful he might actually take him out the country and may never bring him back!!