I get no error and the part does not get cloned into all players character.
game.Players.PlayerAdded:connect(function(Player)
Player.CharacterAdded:connect(function(Char)
local RS = game.ReplicatedStorage
local Part = RS:WaitForChild("DisplayOverHead")
local Head = Char:WaitForChild("Head")
Part:Clone().Parent = Char
end)
end)

4 comments
Can you pls include the error?
I think you want to put DisplayOverHead to head in character right? So just add Char.Head
I suggest making a weld, that welds the part to whatever you want to stick too
Yup, you need to Weld.