Why do some people have the custom to say, in the blessing on the Chanukah lights, the word "Shel" before "Chanukah" and some do not? And I have been told some people put the words together as "SHELCHANUKAH": why is that?
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As with most issues of nusach, the proper one for you is whichever one your parents or teachers taught you.
Shulchan Aruch (Orach Chaim 676:1) has it without של, but Mishnah Berurah there comments that the Gemara and Poskim include this word, and Maharshal argues that the correct version is שלחנוכה (as one word).
There is a good summary of the various opinions, with sources, in Dayan Raskin's notes on the Siddur of R' Shneur Zalman of Liadi, here (note 8).