spitting in aleinu

what a hallachik, kabbalistick or any other sources to spit in aleinu leshabeach (for those who do it)?

Shalom, There is no rabbinic source for that minhag, and to the contrary, the Talmud Y’rushalmi (ch. 3) cites an opinion that you are not allowed to spit at all in shul, and the Shulchan Aruch (151, 7) allowed it only in a generation when it’s acceptable, and only if you immediately cover it. The Mishna Brura adds there (Sha’ar Tzion 15) that today, when spitting is considered uncouth in one’s home, how much more so that one is not allowed to spit in shul (or even out of shul, if others are around)! The only place I have seen the custom is in Lubavitch (when they say: “lahevel varik” which literally means: “that they (the gentiles) bow to emptiness”, because the word for emptiness, “rik”, sounds like “rok” which means spit), where if it’s accepted there, and really doesn’t bother anyone, than it would be allowed, but only in such a synagogue, which is pretty rare. In summary, there is no source in the sages, and in almost every place and case today, it is forbidden because it is disrespectful. With Love of Israel, Rav Ari Shvat