Occasionally I use Google to check that a word was not previously a word of the day - and as luck would have it, no one has yet discovered abecedarian. An abcedarian can be someone who is learning the alphabet (although, I don't know if this means precisely the English alphabet or any alphabet). It can also mean beginner or newbie in that regard.
As an adjective, abecedarian can also be a synonym for alphabetically or anything relating to the alphabet. I suppose if you wanted to sound particularly well-read and obtuse, you could ask someone to organize objects in an abecedarian way.