I know that the time on a moving object moves slowly compared to a stationery one, but if someone on a spaceship that moves at V=0.5c and a person is driving it. Will he notice that the clock on his spaceship moves slower or he will feel the same as he was stationer.
The way to answer this question is to ask how does the person in the spaceship know they are moving at half the speed of light, other than by looking out of the window? They don't: so all the laws of physics are the same for them as for anyone else, and their clock keeps perfectly good time.
Since you already know that moving clocks run slow, you can use a symmetry argument to answer your question. If the spaceship is moving with half the speed of light relative to you, then you are also moving with the same speed relative to the spaceship. From your point of view a clock on the spaceship is running slow. From the point of view of the spaceship, your clock is running slow.
In the spaceships frame of reference the stationary onboard clock will run faster than your clock when you move it but first noticeable if you had a really, really fast bike. If you don't move at all, the clocks will show the same time no matter what speed the spaceship has according to the ground controller or the captain, but the ground controller will think the onboard clock is slow.