In the scenario you described, where you are moving at a high speed relative to a clock far away, both you and the observer on the clock would perceive time dilation. This situation demonstrates the concept of relative motion and the relativity of simultaneity.
From your perspective inside the spaceship, the clock far away would appear to be ticking slower. This is because, in your frame of reference, the distance between you and the clock is contracted due to your high velocity relative to it. As a result, it would take longer for each tick of the clock to reach you.
From the perspective of the observer near the distant clock, your clock onboard the spaceship would also appear to be ticking slower. This is due to your high relative velocity with respect to the observer. Time dilation is symmetric, meaning that each observer will perceive the other's clock as ticking slower.
These observations might seem contradictory, as each observer believes that their own clock is "correct" and the other clock is ticking slower. However, this apparent contradiction is resolved by understanding that there is no absolute "correct" time. Time is relative and depends on the observer's frame of reference.
The phenomenon of time dilation arises because the speed of light is constant for all observers, regardless of their relative motion. The constancy of the speed of light is a fundamental postulate of special relativity. As a consequence, when objects are in relative motion, their measurements of time and space will differ, and time dilation occurs.
Therefore, time dilation is a relative effect. Different observers moving at different velocities will perceive time to be dilated for each other, leading to apparent discrepancies in the ticking rates of clocks. This is a consequence of the underlying principles of special relativity and the relativity of simultaneity.