Well, "alumni" would refer to anyone who went to the same school without regard to being in at the same time and "the class of ___" would limit it to students that were in the same year, i.e., a freshman when you were a freshman, etc. I don't know of any single word that covers this concept, but then I don't know every word in the English language. There may well be a word that covers this concept but is only used by some small subset of the people covered by the word. It may, for example, be used only by students at Boogaloo State and is unheard of in other venues.