Dates on US paper money can be very difficult to interpret. Unlike dates on coins that (usually) indicate the calendar year in which they were minted, dates on bills are "series dates" that indicate the year that a particular design and/or signature combination was adopted. The series date remains the same until the Treasury Department determines that a new series is needed.
Up till 1974 the general practice was to change a denomination's series date only when there was a major redesign. When a new Secretary of the Treasury or United States Treasurer took office during that series, a small letter would be added next to the date.
Because the 1935 series of $1 bills was never redesigned the Treasury kept incrementing the letter every time a new official was appointed. The rather absurd result was that bills printed as late as the mid-1960s still carried a 1935 date while the series letter increased to H. The approximate issue dates are as follows, and shows that your 1935E bill was in fact printed during Ms. Priest's tenure.
In response to that situation the policy was changed in 1974 so that a new series would start when either a new design was adopted OR a new Secretary of the Treasury took office. The letter would increment only when or if a new Treasurer was appointed during a given series. If you check the bills in your wallet you'll see that changes in series dates are now much more frequent and series letters rarely go beyond A or B.
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The series 1917 "George Washington" United States Note is not a Silver Certificate. There were no "Silver Certificate" notes printed with the series 1917. The series of "Silver Certificate" notes used during that time had the date of 1899 or 1923. The 1899 Silver Certificate had a "Black Eagle", and the 1923 Silver Certificates had "George Washington" on the front, respectively. The 1917 "George Washington" United States Note have five different set of signatures. These signatures are signed by the Register of the United States and the Treasurer of the United States. They are Teehee & Burke, Elliott & Burke, Burke & Elliott, Elliott & White, and Speelman & White. The values for these notes vary depending on who signed the notes, the condition of the note, and the grade of the note.
The United States did not print a 1915 $10,000 gold certificate.
There are no signatures on a US 1 dollar bill. The dollar bill features the signatures of the Secretary of the Treasury and the Treasurer of the United States on the bottom right side. However, these signatures are printed rather than physically signed.
In July of 2014, the Secretary of the Treasury of the United States was Jacob Lew. He is the 76th person to hold that position.
Its red ink indicates your bill is a United States Note and not a certificate. Certificates were issued for gold, up to 1933, and for silver, up to 1957. None were dated 1963. There's more information at the Related Question.