mid-14c., conisance, "device or mark by which something or someone is known," from Anglo-French conysance "recognition," later, "knowledge," from Old French conoissance "acquaintance, recognition; knowledge, wisdom" (Modern French connaissance), from past participle of conoistre "to know," from Latin cognoscere "to get to know, recognize," from assimilated form of com "together" (see co-) + gnoscere "to know," from PIE root *gno- "to know."
Meaning "knowledge by observation or notice, understanding, information" is from c. 1400. In law, "the exercise of jurisdiction, the right to try a case" (mid-15c.). Meaning "acknowledgment, admission" is from 1560s. The -g- was restored in English spelling 15c. and has gradually affected the pronunciation, which was always "con-." The old pronunciation lingered longest in legal use.