Ron Guth: In 1893, dies were manufactured for S-Mint Barber Quarter Dollars with the mintmarks shifted to the right. This mitigated the problem of die chipping that resulted from the centering of the mintmark on the 1892-S Quarter Dollar. Researchers have noted two different mintmark positions on the 1893-S Quarter Dollar: one with the S positioned above the space between the R of QUARTER and the D of DOLLAR and another with the S positioned above the left edge of the D. Examples of both can be seen by clicking on the "View All Images" link.
Sources and/or recommended reading:
"Those Shifty Mintmarks" by David Lange, The Numismatist, September 2010, pp. 21-22