Tile top table repair

I have two tile top tables with broken tiles.
I have been unable to find tiles the correct size or
Thickness. One requires 5-7/8" square tiles 3/16" thick. One requires 4-1/4" square tiles 5/32" thick.
It seems that standard tiles are 1/4" thick.
I have had tiles cut for the 5-7/8" square, but these
Are too thick and sit up above existing tiles.
Does anyone know if tiles can be bought as I describe, or do I have to travel to malaysia to find?
(origin of tables I suspect)
thanks

dgouldman@cnkmachinemfg.com

You're wasting your time. Repair it with something close and forget it. There is no such thing as a "standard tile size".