Who was the first US presidential candidate to be assassinated during the election campaign?

The first assassination attempt during an election campaign occurred in 1912 against Theodore Roosevelt, when he ran as the standard-bearer for the Bull Moose Party after being out of office for four years. He survived the attempt as did George Wallace in 1972.

In 1968 Robert Kennedy was assassinated in Los Angeles after a major victory in the California presidential primary.

https://sgp.fas.org/crs/misc/RS20821.pdf

Happened much earlier in 1844.

The 1844 assassination referred to by peninhota, above, appears to be that of Joseph Smith Jr., the founder of Mormonism. He and his brother, Hyrum, were killed while in jail having been arrested on charges of incitement to riot, which were later escalated to charges of treason.

https://en.wikipedia.org/wiki/Joseph_Smith_1844_presidential_campaign
https://en.wikipedia.org/wiki/Killing_of_Joseph_Smith