Connecting spray head to sink supply tee

[Sukhoi]

I am trying to connect a spray head with a 1/4" FIP hose to https://www.brasscraft.com/product/38-in-o-d-tube-x-38-in-o-d-tube-x-38-in-female-comp-nut/ . The faucet connects to the other 3/8" male compression side. Thus I need an adapter with female 3/8" compression on one end and 1/4" MIP on the other. Does this exist? I've looked all over McMaster and BrassCraft and can't find anything. I'll even take female 1/4" compression to 1/4" MIP as I have that same damned tee with a 1/4" compression side outlet.

Or if someone can find a tee like that with any sort of MIP connection on the side.

Edit: Amazon Q&A for the spray head hose says it may be 5/16" FIP not 1/4" like the specs say. But 5/16" isn't even a valid pipe thread size. I can say the hose is much larger than the 1/4" compression fitting, and barely too small to fit over the 3/8" compression fitting.

 

[boomerang]

So you want to tee into a 3/8 supply line and have a 1/4 MIP to connect sprayer to, correct?

https://www.ebarnett.com/Sku/272418...MI29qDu-Lj1wIVnbrACh1nXAkgEAQYAyABEgLxfPD_BwE

 

[Sukhoi]

Well I want to put a tee on the output of a 1/4 turn valve. The valve is directly mounted on the wall, and then currently the 3/8" compression hose to the faucet is attached. I want to put a tee in there so I can also attach the 1/4" FIP hose for the sprayer.

If somehow this type of tee or a female compression to NPT adapter doesn't exist, I'll have to cut the 1/4" FIP off the hose and replace it with a female compression fitting so I can use it with the tee I already have.