What is the medical term meaning fat pad of the hand under the thumb?

Answer 1

Ephippium policis

Coxa is latin or ephippium (greek and later accepted in latin) is for pad (cushion)

Thumb is Polex (pollicis plural)

Thumb: The short thick digit of the human hand, next to the index finger and opposable to each of the other four digits.

Pad: The cushionlike flesh on the underpart of the toes and feet of many animals.

Polex is the latin term for thumb (like in musculus abductor pollicis, or priceps pollicis brevia)

Answer 2

Thenar eminence.