Depending on condition, it's a contest between those minted in 1877 and those from San Francisco dated 1909.
There's more information at the Related Questions.
Indian head penny
Indian head penny
The two rarest Indian Head pennies are the 1877 and the 1909-S.
The Indian Head penny was not minted until 1859.
There was never a silver Indian Head penny.
There is no such coin as a Indian Head Buckwheat penny, but a 1898 Indian Head cent in average condition is worth $1.00-$3.00
1865 would make it an early Indian head penny, not a Lincoln wheat penny. It's not the rarest of dates. In worn condition it's worth around $10, and in uncirculated condition it's worth a little over $100.
No 1803 Indian Head penny's exist. The first one was struck in 1859.
1874 Indian Head Penny: good condition-$13.00, mint condition-$155.00
The Indian Head penny wasn't minted in 1801. The coin was minted by the United States Treasury between the years of 1859 and 1909. An uncirculated 1901 Indian Head penny is valued at $30.00.
The last Indian Head penny was made in 1909, look at the coin again and post new question.
Before the Indian Head penny, the United States minted the Liberty Head penny, also known as the Flying Eagle penny. The Liberty Head design was used from 1856 until 1858, while the Indian Head penny was introduced in 1859. The Liberty Head featured a classic depiction of Lady Liberty and was part of the larger cent coinage reforms during that period.