As far as I’m aware, Mansa Musa’s immediate predecessor, Mansa Muhammad, is believed to have disappeared after setting out on a voyage across the Atlantic Ocean in the early 1300s (so prior to Columbus’s voyage). I am not aware of any African expeditions after Columbus, though.

As for Asia, I’m not aware of any Asian expeditions, but it should be noted that most Asian countries had far further to travel, in a less favourable direction (sail boats can cross the Pacific more easily sailing from the Americas to Asia, than from Asia to the Americas, and have less trouble travelling from Europe to the East coasts of the Americas) and Asia was generally fairly wealthy already, and therefore had less need to travel around the world searching for spices and cities of gold, as they already had spices and silk. Europeans, on the other hand, were attempting to gain access to Asian markets and wealth in the early modern era, and we’re also attracted to the land and resources of the Americas as a further new source of wealth. So many Asian states lacked a serious incentive for exploration.