Have problem with create puzzle game

Hello! I decided to try to create a puzzle-style game. But I was faced with a funny situation, I don’t understand how to check objects on the figure field and so that the figures automatically adjust to the cell. I attached a GIF picture to clearly show what I want.

I made a regular Drag, when transferring shapes to a cell, there are no checks; I have no idea how to do this. And how to organize the playing field.

P.s. I used UI and canvas.