I assume you mean a digital clock and that it only displays hours and minutes, not seconds. I'll also assume it's set to standard AM/PM time, not 24 hour time, which would be a bit different.
The times that would display exactly three 1s are:
That's 17, and they would be displayed 2x per day each, so 34 minutes in total.
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A 24 hour clock displays digits whose sum total equals the number of led's used to display them 94 times a day. A 12 hour clock displays them 108 times a day.
On an analog clock with a 12-hour face: 44 times. On a digital clock: zero. (No needles.)
5 times
Exactly three times
Exactly 55 times