To expand upon the question, there are plenty of definitions of what people consider a "gun." So I might split it into several questions, on the off-chance someone can better answer one over the other.

Who (or when) was the first person killed by a...

• Gunpowder-based projectile

• Handheld (small arms) gunpowder-based projectile

• Gun that uses rounds (i.e. self-contained shells with gunpowder, bullet, and ignition mechanism)

• Automatic weapon

"Who" might not necessarily mean a name, but maybe which kind of person (e.g. civilization, year, social status)?

As others have said it is hard to tell what specifically it is that you are asking, but if you are asking about the first assassination by firearm I can tell you that.

In Scot land James Stewart, 1st Earl of Moray was assassinated in 1570 by James Hamilton of Bothwellhaugh. James Stewart was the regent for James VI of Scotland, but at this time Scotland was engulfed in a civil war. James Hamilton of Bothwellhaugh was a supporter of Mary of Guise (the opposition to the infant James VI), so when he found an opportunity to fire at him with a carbine from his uncles home, he did so, fatally wounding James Stewart.

Sources: (It is hard to find any definitively reliable source, but there are many different sources that agree.)

Antonia Fraser, Mary, Queen of Scots, pp. 339, 486

https://artemisiasroyalden.wordpress.com/2013/01/24/day-in-history-james-stewart-is-murderd-in-the-first-recorded-assassination-by-a-firearm/

http://www.maryqueenofscots.net/people/lord-james-stewart-earl-moray-regent-scotland/

If anyone has any definitively reliable sources, a reply would be greatly appreciated, along with any corrections.

Remember, for a long time (in Europe at least) the only guns were siege weapons. So it's unlikely that anyone would record which unlucky 13th-century foot soldier was the first to be crushed by a flying cannon-boulder. And that's not even considering China, which had had gunpowder rockets for quite a while at that point.