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-- ServerScriptService > CoinServer (a Script, so it runs on the server)
local ReplicatedStorage = game:GetService("ReplicatedStorage")
local Players = game:GetService("Players")
local collect = ReplicatedStorage:WaitForChild("CollectCoin")

local MAX_DISTANCE = 8   -- studs
local COOLDOWN = 0.5     -- seconds
local lastPickup = {}

local function onCollect(player, coin)
	if typeof(coin) ~= "Instance" or not coin:IsDescendantOf(workspace.Coins) then return end
	local root = player.Character and player.Character:FindFirstChild("HumanoidRootPart")
	if not root then return end
	if (root.Position - coin.Position).Magnitude > MAX_DISTANCE then return end
	local now = os.clock()
	if lastPickup[player] and now - lastPickup[player] < COOLDOWN then return end
	lastPickup[player] = now
	coin:Destroy()   -- gone for everyone, so it cannot be taken twice
	player.leaderstats.Coins.Value += 1
end

collect.OnServerEvent:Connect(onCollect)
Players.PlayerRemoving:Connect(function(player) lastPickup[player] = nil end)

Put a RemoteEvent called CollectCoin in ReplicatedStorage, a folder called Coins in the workspace and a leaderstats folder with a Coins value on each player. We have not run this script outside Studio; the checks are mirrored in the Python twin below, which we did run.

import math

MAX_DISTANCE = 8   # studs
COOLDOWN = 0.5     # seconds

coins = {"c1": (10, 0), "c2": (30, 0), "c3": (50, 0), "c4": (200, 0), "c5": (204, 0)}

# requests the server receives: (time, player, coin, where the player really stands)
requests = [
    (1.0, "Mia", "c1", (12, 0)),
    (3.0, "Mia", "c2", (29, 0)),
    (5.0, "Mia", "c3", (55, 0)),
    (1.1, "Cheat", "c4", (0, 0)),     # claims a coin 200 studs away
    (1.2, "Cheat", "c1", (10, 0)),    # coin already taken
    (2.0, "Cheat", "c9", (0, 0)),     # a coin that does not exist
    (6.0, "Cheat", "c4", (199, 0)),
    (6.1, "Cheat", "c4", (199, 0)),   # same coin twice
    (6.2, "Cheat", "c5", (200, 0)),   # next coin a fifth of a second later
]

trusting = {}
for t, player, coin, pos in requests:
    trusting[player] = trusting.get(player, 0) + 1
print("If the server believes every request:", trusting)

taken, last, score = set(), {}, {}
reasons = {}

def check(t, player, coin, pos):
    if coin not in coins: return "no such coin"
    if coin in taken: return "already taken"
    if math.dist(pos, coins[coin]) > MAX_DISTANCE: return "too far away"
    if player in last and t - last[player] < COOLDOWN: return "too fast"
    return None

for t, player, coin, pos in sorted(requests):
    why = check(t, player, coin, pos)
    if why:
        reasons[why] = reasons.get(why, 0) + 1
        continue
    taken.add(coin)
    last[player] = t
    score[player] = score.get(player, 0) + 1

print("With server checks:", score)
print("Rejected:", reasons)

It prints If the server believes every request: {'Mia': 3, 'Cheat': 6}, then With server checks: {'Mia': 3, 'Cheat': 1} and Rejected: {'too far away': 1, 'already taken': 2, 'no such coin': 1, 'too fast': 1}.