What size pipe fitting has an outside diameter of about 1/2 inch?

So in another thread this week I asked a question about the type of valve I need but I ordered the wrong size…uggh.

I ordered this tee connection because it included a shut off valve…which I like.

The new valve thread (3/8") is too big for the existing nut. Can someone help me confirm the correct size I need this time?

Half inch (see photo) minus 1/4" for threads = 1/4"…?