Given you used condoms, it is unlikely he is the father - but not impossible. If it is his child, then he has rights. You may not have the option of permitting him - or not - to be in your lives. But he does not have to be in your life as bf.
His gifts are not gifts as they are given with strings attached - the buying of your affection. He feels when he gives you something that you owe him. This is controlling and not the basis of a healthy relationship. Refuse the gifts. Give back what you can. End it.