There isn't such a thing as "small goldfish". Normal goldfish can grow to 12"+, while fancies can easily reach 6".

How shallow you can have the water depends on the other dimensions. Plus you have to be able to practically fit in a heater, filter etc. I'd personally say an 8" heigh tank would be minimum.

 

Oh, i no nothing about fish really i will have a look on the internets.

 

As said, goldfish are not small, yes you get babies but they should grow large, up to and excess of a foot long depending on type. Only stunting their growth will keep them small, and it isnt healthy for them. Guppys, small tetras, small rasboras can be kept in smalle tanks but they need to be in groups so larger bodies of water are far better for them. A siamese fighter can do ok in a smaller tank, but will use the space if given larger so keeping them in smaller does seem an awful thing to do to me. Also, the larger the volume of water, the easier it is to keep the water healthy for the fish.

Whatever fish you want to keep, no matter how small, the water will need to have a filter running in it 24/7 so that itself will limit the minimum depth you have.

 

I keep White Cloud Mountain Minnows in 6 inches of water........with my Emys.

As said above the filter must run 24 7.........and they have loads of rock and wood and weed to dart about through to avoid ending up on the inside of Emys!
All the best!:smile::smile: