If so, how were they trained and equipped? Were they effective?
Alright, I've had to remove a lot of answers in this thread for the same reason: one sentence, speculative responses are not welcome on this subreddit. If all you can say about this topic can fit into a single sentence, we'd prefer it if you just don't post.
I'm not sure I really understand the question.
Are you asking if armies dispatched archers in very small squads to attack high value targets from an ambush point, as opposed to having large offensive lines of bowmen?
Or are you asking if there were special bows that allowed for shooting over much greater distances than conventional archers?
But then, "conventional archer" is a loaded term because there have been many different types of archers over the ages. I could talk more about this, but I should probably check back on my sources first.
I'm not sure if this is what you were looking for but I found these examples in the Medieval Middle East.
"When the mamluk units themselves charged against Mongols they sought close combat so that they could bring their heavier spears, swords and maces to bear. If they did reach the enemy lines, selected archers shot down the foe's standard bearers and drummers to deprive him of battlefield communication"
p.14 Nicolle, David. The Mamluks 1250-1517. Osprey, 1993.
" Selected marksmen could harass the foe before a general engagement - as was attempted at the battle of Arsuf in 1191. Tactical manuals suggested that sharpshooters try to bring down enemy leaders. Written records also show that an enemy's communications, as well as his morale, could be undermined by shooting or otherwise overthrowing his drummers or standard-bearers."
p.28 Nicolle, David. Saracen Faris 1050-1250AD. Osprey, 1994
Followup question: Would the need for handpicked marksmen/"snipers" not have come around till much later on? I've always thought that, at least in European warfare, officers (or nobles, earlier on) were more or less "off limits" and were not to be specifically targeted. As such, would there be no need for single marksmen to go after "high priority" targets?