A question about TickRate and other input (like a shot)

Let us assume a TickRate of 60. This means that there is 16.666 ms between ticks.

What happens with input other than movement? For example a sniper shot? When the button is pressed on the client, it will take potentially 16.666 ms before the shot is being sent.

In a fast paced game that can make the difference between a headshot and a whiff. Is it possible to send the input as a fraction of a tick? F.ex. that the shot was fired at TickRate + 6 ms? And is it something being done in games?