The various types of asteroids spawn according to "temperature." This temperature varies depending on the heat of the star and the distance from the star. Star systems with smaller, more red stars are colder and sometimes cannot spawn asteroids that require heat while stars that are very large and blue might not spawn any that require cold.

Remember that systems claimed by your faction give a 12x ore bonus and if claimed by another faction then it gives a 6x bonus


Below is a simple chart to tell you where to find your minerals. The labels show what type of asteroid is generally there and they are colored to match their respective asteroid.