On Mac: Control+Shift+mousedrag moves in the finest increments (ticks). You must press Shift after the mouse has been clicked on the object.

On PC: Alt+Shift. You need to click on the object first before pressing Alt+Shift.

Omitting the Shift key will move in "divisions", as set in the box below the time signature in the Transport window.

You can also set a nudge shortcut with a key command (type "nudge" in the Find box in the Key Command window). You have choices of ticks, bars, beats, resolution, frames, half frames etc.