What is the smallest length marked on a 12-inch ruler?

This depends on the ruler. Some rulers show only inches, in which case the smallest length would be one length. Some even mark half, quarter, eighth, etc. inches so those would be even smaller. However, the standard 12 inch ruler will have marks as small as sixteenth inches. Therefore, the smallest length would be 1/16 inch.

Not all 12-inch rulers are the same.

I have one with no marks smaller than 1/4 inch, and I have another one

with the first inch marked in 64ths of an inch.