The type "B" are the proof reverses that were re-used on the 1956-64 Philadelphia quarter reverses.

So your coin is too early and not a Philly coin to be a type "B".
Mint marks are added to the dies and hand punched. They can be in various locations and in varying strength. Some years had different styles of mint mark punches, but there were on the "S" quarters. Hope this helps.