Option 1 -> "for your watch" implies purpose, which is grammatically incorrect in this context.
Option 2 -> "at your watch" is not idiomatic English and sounds unnatural.
Option 3 -> "by your watch" is the correct idiomatic expression meaning "according to your watch."
Option 4 -> "from your watch" doesn't work as it suggests origin rather than reference.
Hence, Option 3: by your watch -> "By" is used to indicate reference or standard of measurement. The phrase "by your watch" means "according to what your watch shows" and is the standard idiomatic expression in English when asking someone what time their watch displays. -> correct