I have java swing chess application. Cursor has custom view – rectangle, sized to fit whole cell. And I need cursor moving only over whole cell. Not in the limits of one cell. Is there some typical solutions for this problem? Or maybe it is possible to set with standard java capabilities step-type cursor moving?

I wouldn’t implement some kind of “stepping” cursor. Instead I would hide the cursor completly and highlight the current cell programmatically.
paintComponentmethod of your custom componentFull example below that “outputs” this screenshot:
And some test code: