Connect 3/8" NPT (National Pipe Taper) to 1/16" NPT (National Pipe Taper)

Stepping a 3/8-18 NPT port down to a 1/16-27 NPT fitting uses a NPT (ASME B1.20.1) reducing bush: a male 3/8-18 NPT on the outside and a female 1/16-27 NPT inside, both to the same NPT form so they seal on the thread flanks with PTFE tape. The major diameter goes from 17.15 mm at 3/8-18 NPT to 7.94 mm at 1/16-27 NPT. This is a single stocked reducing part; the step is three nominal sizes.

Both ends are the same NPT standard, so the only thing that changes is the size; do not swap standards at the same time. If you need to cross to a different thread form as well, add the correct thread adapter rather than forcing a same-standard reducer to do two jobs.