Question

which stars remains fixed at one place

Answer 1

actually all stars move. but polaris seems to be fixed because it revolves similarly to sun in the space that makes it appear to be fixed.

Answer 2

The fixed stars are celestial objects that do not seem to move in relation to the other stars of the night sky. Hence, a fixed star is any star other than the Sun. A nebula or other starlike object may also be called a fixed star. People in many cultures have imagined that the stars form pictures in the sky called constellations. InAncient Greek astronomy, the stars were believed to exist on a giant celestial sphere, or firmament, that revolves daily around Earth.