"by me" or "by I"

[jimthecanoeist]

Is “by” still a preposition used to answer “written by me" or "written by I”? Here we are not using “by” to indicate where the writing was accomplished (a sure usage as preposition meaning “close to me”) but rather as denoting who accomplished it (“I wrote it”). “Written by I” sounds stilted and I would use “written by me” but unsure what grammatical authority governs.

[Alan]

There is no occasion on which it would ever be correct to say 'by I'.