Fill in the blank with appropriate preposition and give a reason:
What is the time _____ your watch?
The best and most correct choice for the blank is the prepositional phrase, according to:
The New Oxford American Dictionary defines according to as:
If you only had one-word prepositions to choose from, then on would be your next best option, although I would not consider it as formal:
Also, using on is a loose way of saying:
You could also use by, although this usage is not common in this context:
One of the definitions of by, as given by the New Oxford American Dictionary, is:
Yes, the technically correct answer is "on," but the question itself is not idiomatic English. That is, you'd never see it in print or hear it spoken by a native speaker. More common would be:
Depends on what you are trying to say
would be the same as asking, "what time do you have?"
would, while sounding a little awkward, be specifying that I seek the time according to your watch rather than someone else's.
would, while also sounding awkward, be asking when the watch was made.
I expect you want the first one, though I might suggest you rephrase saying:
That implies that you suspect that watch may disagree with someone else's (either because it is wrong, or the other watch is).