THE TAYLOR SMITH & TAYLOR CO EAST LIVERPOOL OHIO. From 1904 Book & Page noted below: "The Smith Lee & Smith Co incorporated in 1899 was the predecessor (at the time of publication of Barber's book in 1904 noted below) Taylor Smith & Taylor Co main product is semi vitreous porcelain. The principal product is semi-vitreous porcelain. Subjoined are the marks of the original company, for semi porcelain and white granite. The new began operations on October 1 1901." You can see the original marks in Barber's book at books.google.com.
Marks of American Potters by Edwin Barber (1904) (Google.books) P.116
The original TST pottery mark looks like a chimera standing over the letters T S T, all in separate circles. The shard I posted has three numbers on it, also states: Made in the USA. The numbers are 2, 35, '2. It leads me to think that the shard is perhaps from 1902.