How would I create a table of players within a certain distance to a part?

You can use DistanceFromCharacter to get the distance from the character's head.

local turret -- define turret
local radius=20

local list={}
for _,v in pairs(game.Players:GetPlayers())do
    local dist=v:DistanceFromCharacter(turret.Position)
    if dist~=0 and dist<radius then
        list[#list+1]=v
    end
end

DistanceFromCharacter will return 0 if the distance cannot be found for some reason (no head/no character.)