Supremacy is a noun and is obtained from the word supreme. Something superior or of high quality is supreme. The quality that such a thing possesses is termed supremacy. For example: he held supremacy in the field of defence research. Here, supremacy indicates eminence or mastery. He is recognized in the field of defence research as a knowledgeable and genius person.
Supreme power or dominance one establishes or possesses is also termed supremacy. For example: he established his supremacy in the desert. Here, supremacy suggests his authority or domination.