When was a 1935 D series 1 dollar silver certificate printed?

The D series was printed between June 1949 and January 1953.

To explain the large difference in dates, up till 1974 the Treasury only put a new series date on bills when there was a major design change, as opposed to the current practice of starting a new series date for each Secretary of the Treasury. The only change to the design of the original 1935 series was the addition of the motto "In God We Trust" in 1957, which the Treasury felt didn't warrant a new date. The 1935 series was printed until the mid-1960s and became the longest-lived date on any bills.

To explain the existence of a similar 1957 series, the Bureau of Engraving and Printing bought new printing presses that were mechanically incompatible with the old presses. They opted to put a 1957 date on bills printed by the new presses while continuing to use 1935 for bills made on the older presses, even though both bills used the same design.