Spell out numbers (years are an exception to this, by the way) instead of using numerals: two hundred (NOT two-hundred) instead of 200.
Population, although referring to a group, is a singular noun (just one group, not more than one), so change have to has.
In the near future, we’ve discovered a way to prolong life by two hundred years, but only for a part of the population that has a specific mutation. You just found out the results of your gene test.
And now, the science-and-common-sense part of the post…
We have the ability to use gene therapy now to change the DNA of some people with genetic defects. It’s not perfect, but it isn’t fiction. In the near future, if it’s discovered that only people with a certain gene can take advantage of some extreme life-prolonging treatment, you betcha there’ll be a lot of people clamoring for gene therapy to get that gene added to their own DNA. Either that, or people who have that gene will be hated by everyone else and sometimes even killed.
Notice the indefinite article a before part of the population? I’d considered changing it to the, but then I realized it implies that the longevity treatment isn’t available to everyone who has that “specific mutation,” only to some people. Yes, folks, even such a small thing as a/an versus the can change the nuances of meaning within a sentence.