a.s.p. is one of the abbreviations that carries more than one meaning. Written out, it can be alto sul ponticello or a.s.p — 2 separate directions that happen to shorten to the same letters. The score itself decides which: the surrounding passage, the instrument, and what the music is doing at that moment.
a.s.p.
In a score, a.s.p. can stand for alto sul ponticello or a.s.p. Here is how to tell them apart.