The cable channel formerly known as the Science Fiction Channel has a new series, The Expanse, which is pretty adroitly done, despite overuse of the trope of "blowing people away" (via pistol, railgun, or airlock), which occurs with as much regularity and emotional impact as a Moe/Curly face slap. The series adapts books by two sf late colonizers writing under the name James S.A. Corey. When it's time to borrow, borrow from the best, and the Coreys owe a large debt to earlier writers for their conception of "the Belt" (as in, asteroids) and Belters.
Larry Niven used "Belter" in the '60s, mostly in short stories in his "Known Space" series. Wikipedia's summation:
The Sol Belt possesses an abundance of valuable ores, which are easily accessible due to the low to negligible gravity of the rocks containing them. Originally a harsh frontier under U.N. control, the Belt declared independence after creating Confinement Asteroid, a habitat with spin gravity that permitted safe gestation of children, and Farmer's Asteroid, the Belt's primary food source. Almost immediately a lively competition began between the fiercely independent "Belters" and the technology police of the U.N. Several years of tension and economic conflicts followed, but soon settled into a relatively peaceful trade relationship as the Belt has so many resources that the UN and the Earth need.
C.J. Cherryh also had gritty Belters in her books Heavy Time (1991) and Hellburner (1992). Wikipedia, again:
[The novels] are set in the Sol system at the beginning of the "Company Wars" period in the 24th century. Heavy Time introduces ASTEX, a division of the Sol Station Corporation, ... engaged in asteroid mining for minerals to support the Earth's economy and the war effort. Disputes over mining rights, corporate corruption and economic exploitation are key plot elements in the first novel.
Both Niven and Cherryh depict Belters as scrappy, independent operators, comfortable in tight spaces and hard vacuum suits, mining the rocks and constantly struggling with more sedentary Earth bureaucracies. The whole concept is basically bunk since radiation exposure and bone density loss make it impossible for humans to live in space for long periods, but as long as romantic conceptions are dying hard, might as well acknowledge the early dreamers.