We do not know of a basis proving the legislation of the ta’awudh or the basmalah before the adhaan – not for the one calling the adhaan nor for the one who hears it. And it is indeed established from the Messenger of Allaah sal Allaahu alaiyhi wa sallam that he said:
Whoever does an action which is not from our affair then it will be rejected.
And in another narration:
Whoever brings something new into this affair of ours which is not from it, then it will be rejected.
And with Allaah is the tawfeeq. And may peace and blessings be upon our Prophet Muhammad and his family and his Companions.