How to Restrict Movement of a Dragged Object to a Game Board?

New to Unity and Scripting... I would like a simple example of restricting the movement of a dragged object to a game board (or other surface). I am either terrible at searching or there aren't many simple examples out there (probably the former).

I have a game grid with various height blocks. I want to drag a chess piece like object over this grid and have it snap to the game grid below the players finger.

I can't just restrict the movement to a plane as the game grid is at different heights.

Any help is appreciated...