I'm not sure what you mean by "hand autographed". If you are referring to the standard signature reproduction on the bill, a 1935G silver certificate (actually printed in the 1950s) would only be worth about $2 if it is as worn as your question seems to indicate.
If however it has Ms. Smith's personal signature in addition to the reproduction, you'd have to take the bill to an autograph collector for an appraisal. Unfortunately, my guess would be that there is not a thriving market for the signatures of U.S. Treasurers, but your note would still be more valuable simply as a curiosity.
Whats the value of a 1935g one dollar bill with blue writing on it
$2 to $3 in average condition
About six dollars
In average circulated condition, about $1.50 If nicer, about $4.00
It is worth ≈ $10
You probably mean 1935G, and most sell for between $1.50 and $5.
The late series letter indicates this bill was actually printed in the 1950s despite the date. The lack of tears would make it worth a couple of dollars at retail. Please note that a bill's serial and check numbers almost never affect its worth. The date, series letter, and condition are the major factors determining value.
My Black Book is a few years old, but it lists this note's retail value at $11 in uncirculated condition. Average dealer buy price for a used example is about $1.60. It's actually worth a little less than the one with the motto.
The 1935 series of blue-seal $1 silver certificates was actually printed until the mid-1960s without a change in date, so there are many varieties to choose from. Check for a small letter next to the date. That's the "series letter" and helps determine when it was actually printed. Despite their age, many 1935 silver certificates remain common among collectors and don't command a huge premium. Auction values as of 09/2009: 1935: circulated, $4.-$7.; uncirculated $18.+ 1935A: $2.-$3.; $18.+ 1935B, C, or D: $2.25-$3.; $13.+ 1935E, F: $1.50; $7.+ 1935G without "In God We Trust" on the back: $2.25-$3.; $10.+ 1935G with "In God We Trust" on the back: $2.25-$3.; $10.+ 1935H: $1.50; $7.+
"In god we trust" is a national motto of the United States and has to appear on all banknotes, by law, since 1955. While the motto first appeared on 2¢ pieces in 1864 and had been on all coins since 1938, it was never printed on bills. Cold-war patriotism led Congress to authorize its addition to bills as well. The first notes with the motto were Series 1957 and 1935G $1 silver certificates that entered circulation simultaneously in 1957. Over the next several years it was added to all other denominations.
The motto In God We Trust was added to 1935-dated $1 bills starting in 1961. The change was made in the middle of the G series printing without changing the series letter or date because it was not deemed to be a major redesign. As a result there are two sub-series of 1935 G $1 bills, the "without motto" and "with motto" notes. The motto appeared on 1957-dated bills from the start of that series in mid-1957. The fact that both dates were used concurrently on bills with the same design came about because different printing methods were used, and is an exception to the practices governing series-date changes both at that time (major redesign) and today (redesign and/or a new Treasury Secretary).
All US bills from the 1920s onward carry a "series" date but not the actual printing date. The series date is in roughly the same place on all bills, normally to the right of the portrait. Determining roughly when a $1 silver certificate was printed can be slightly difficult. Up till the 1970s, the Treasury tended to change series dates only when a bill was redesigned, and the 1935 series used the same design from its introduction until it was discontinued some thirty years later! Here's a list of approximate printing dates, based on the letter next to the year: 1935, 1935A : 01/1935 - 07/1945 1935B : 07/1945 - 07/1946 1935C : 07/1946 - 05/1949 1935D : 06/1949 - 01/1953 1935E : 01/1953 - 07/1957 1935F, 1957 : 07/1957 - 01/1961 1935G, 1957 A : 01/1961 - 04/1962 1935H, 1957B 01/1963 - 03/1965