Cohort
Could you be thinking of the word “cohort”? It starts with the letter “C,” and basically describes what you’re thinking of (albeit in a somewhat technical context): a segment of the population sharing some common element. Per Wikipedia:
In statistics, marketing and demography, a cohort is a group of subjects who share a defining characteristic (typically subjects who experienced a common event in a selected time period, such as birth or graduation).
Or, according to Merriam-Webster:
A group of individuals having a statistical factor (as age or class membership) in common in a demographic study.
Community
This seems a little obvious, but it does start with a “C” and end in a “y,” and can describe a certain group within a population (“the medical community,” “the local community,” “the Scrabble-playing community." According to Google’s definition:
A group of people living in the same place or having a particular characteristic in common.