What is the value of a 1937 H US 1 dollar silver certificate?
Please check your bill again. There are no 1937-series US bills.
If the date is 1935, more information can be found at the question "What is the value of a 1935 H US 1 dollar silver certificate?"
A 1937 quarter will have George Washington's portrait on it. You must have a half dollar instead. A circulated 1937 half is worth about $2.88 as silver bullion today (spot silver is $9 / troy ounce). Numismatic value runs from $3 to $5 in Good condition and from $6 to $10 in Very Fine condition, depending on the mint mark.