The scenario you are describing is based on the principles of special relativity, specifically time dilation. According to special relativity, time is not absolute and can be experienced differently depending on the relative motion between observers.
When you are traveling at a high velocity, close to the speed of light, your perception of time will indeed be different compared to someone who is stationary. However, from your perspective on the ship, your clock will appear to be ticking normally. This is because time dilation affects the way you perceive time, not the actual functioning of your clock.
Similarly, from the perspective of the observer who is not moving relative to the ship, their clock will also appear to be ticking normally. Both you and the stationary observer will perceive your own clocks as functioning correctly, even though there is a difference in the passage of time between the two of you.
The reason for this is that time dilation occurs due to the relative motion between two frames of reference. The faster an object moves relative to another observer, the more time appears to slow down for that object. This phenomenon is a consequence of the constant speed of light in all reference frames, as postulated by Einstein's theory of special relativity.
In summary, time dilation is a consequence of the relative motion between observers and is a fundamental aspect of special relativity. It results in differences in the perception of time but does not affect the operation of clocks themselves as experienced by the observers in their respective frames of reference.