Which of the followingis is/are correct/common?
  • he had it at his fingers' ends
  • he had it at his finger's end
  • he had it at his fingers ends
"He had it at his fingertips" is the only similar one that I'm familiar with.

(At least that avoids the messy plural possessives!)
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1st is correct
Anonymous 1st is correct

No. The first reply is correct.