This is an unusual fear, this is the fear of clocks. This is probably one of the rarest phobias there is. I have no idea what triggers this phobia myself, though I know most phobias are caused by traumatic childhood experiences. But what is the basis for an irrational fear of clocks? In my research, I came across a blog of someone who has a friend with this condition. He said that it is a reminder that people are not immortal. Like the majority of fears, the basis for this one is death or suffering.
People do have a paranoia of being late for something, or waking up at a specific time, but paranoia is not the same as a phobia. Paranoia is just an annoyance. People who have chronomentrophobia have a fear of seeing a clock, or experiencing time, or thinking about time. Some people fear a specific time of day, like there is a lot of fear of midnight among chronomentrophobes.
I personally am very fascinated by clocks. When I see a clock, I tend to just stand and look in fascination. Some can be beautiful, mesmerizing and alluring. What home would be complete without a decorative clock? I have several in my home and I love them! If for nothing else, the fascination that they bring me.