The value of a 2 dollar bill is determined by its rarity, condition, and historical significance. While many 2 dollar bills are still in circulation, there are a few specific years that are considered more valuable than others to collectors. In this answer, I will provide an overview of the history of the 2 dollar bill and highlight some of the years that are considered to be more valuable.

The 2 dollar bill was first introduced in the United States in 1862, during the Civil War. At that time, the federal government was printing large quantities of paper money to finance the war effort, and the 2 dollar bill was one of the denominations that was created. However, the 2 dollar bill did not become a regular part of the US currency system until the early 20th century.
The 2 dollar bill has always been somewhat unusual compared to other denominations. For one thing, it has not been printed as frequently as other bills, so it has always been somewhat rare. In addition, the design of the 2 dollar bill has been changed many times over the years, and some of the older designs are more valuable to collectors.
One of the most valuable years for 2 dollar bills is 1899. This was the first year that the bill was redesigned with a portrait of George Washington in the center. The design also included a vignette of the landing of Columbus on the left side and a vignette of the discovery of gold in California on the right. 2 dollar bills from 1899 are quite rare and can be worth several thousand dollars, depending on their condition.
Another valuable year for 2 dollar bills is 1918. This was the first year that the bill was printed with a green seal and serial numbers. 2 dollar bills from 1918 are also quite rare and can be worth several thousand dollars, depending on their condition.
In the 1920s and 1930s, the 2 dollar bill was printed with a variety of different designs, but none of these are particularly valuable today. However, in 1953, the bill was redesigned with a portrait of Thomas Jefferson on the front and a vignette of the signing of the Declaration of Independence on the back. This design was used until 1963 and is still considered to be one of the most beautiful designs for a US banknote. 2 dollar bills from this period are not particularly rare, but they are still popular among collectors and can be worth a premium over face value, especially if they are in excellent condition.
In the 1970s and 1980s, the 2 dollar bill was printed with a design that featured a portrait of Thomas Jefferson on the front and a vignette of the signing of the Declaration of Independence on the back. This design is still in use today, although the bill has been updated with anti-counterfeiting features in recent years. 2 dollar bills from the 1970s and 1980s are not particularly valuable, but they are still popular among collectors.
In conclusion, while there are a few specific years of 2 dollar bills that are more valuable than others, the value of any individual bill will depend on its rarity, condition, and historical significance. 2 dollar bills from the late 19th and early 20th centuries are generally more valuable than more recent bills, but there are exceptions to this rule. If you are interested in collecting 2 dollar bills, you should do your research and look for bills that are in excellent condition and have a strong historical significance.