(anatomy) The finger next to little finger; third finger; ring-finger.
Wiktionary
Origin of Leech-finger
From Middle English leche fingir, læchefinger, from Old English lǣċefinger (“fourth finger, leech-finger”), equivalent to leech (“physician”) + finger. Compare Old Norse lǽknisfingr (“leech-finger”), Icelandiclæknisfingur.