What is the highest series letter on a 1935 US 1 dollar silver certificate?

"H" was the highest letter for Series 1935 $1 bills. That subseries was actually printed in the early 1960s!

Prior to 1974 the Treasury only changed series dates when a bill underwent a major redesign. The 1935 series of $1 bills was never updated so series letters incremented every time a new Secretary of the Treasury or US Treasurer took office. That rather absurd situation led to a change in the criteria for assigning a new series date. Beginning in 1974, the series date changes each time a bill is redesigned OR a new Treasury Secretary takes office; the series letter increments only when a new Treasurer takes office during the administration of the same Treasury Secretary.