The color pattern seen in breed standard Yorkshire Terriers of the steel blue body with tan head and extremities is due to a certain mutation at the ASIP (agouti signalling protein) locus, classically called the "A" gene. Yorkshire Terriers carry the variation of the "A" gene called "at." Interestingly, there are four major variations of the "A" gene:
ay = "fawn" or solid golden-brown
aw = "wolf sable" or hairs that are banded black and brown
at = black and tan, with black body and tan extremities
a = recessive black
Interestingly, the order of dominance is ay > aw > at > a, which means that fawn is dominant to all the other color patterns, wolf sable is dominant to black and tan and recessive black, and black and tan is dominant only to recessive black.
There is a variation of black and tan called "saddle tan", which is due to an interaction of the "at" mutation with mutations at other modifier genes. In saddle tan dogs, the tan coloration comes up farther onto the body than in the black and tan pattern. I'm providing three links to research papers describing these interactions that are publicly available in their entirety below. Although neither of these studies specifically examined the DNA of the Yorkshire Terrier as far as I have read (a quick once-through), they postulate that Yorkshire Terriers are actually a form of saddle tan in coloration, with the tan not coming up quite as far on the body as in other saddle tan breeds. Here are the research articles:
A SINE Insertion Causes the Black-and-Tan and Saddle Tan Phenotypes in Domestic Dogs eCommons - Gene interactions with Agouti Signaling Protein produce complex pigmentation phenotypes in the domestic dog http://www.eebweb.arizona.edu/Facult..._etal_2013.pdf