Clone at mouse position help?

You've misunderstood how mouse move works and how connections work.

Never define a function inside of a loop. There are very rare circumstance where you want to do this, but most of the time you can fix this.

Your start is fine:

obj = script.Parent

We're also going to create an original image copy:

originalImage = obj.Image:Clone()

But then you don't want the loop. What we'll do is we'll keep track of where the mouse is, by defining new variables:

mouseX = 0
mouseY = 0

-- both of these are defaults, where the mouse is before the player puts their mouse over it.

Next, we're going to use the update function to change these to reflect the position of the mouse:

function updateMove( x, y)
    mouseX = x
    mouseY = y
end

This creates a function called updateMove that takes two arguments, x and y. All it does is set the variables mouseX and mouseY to be copies of these.

But on its own, nothing happens. It's just a block of code to be called later. So it won't run yet. We add the connection:

obj.MouseMoved:connect( updateMove )

Now, whenever the mouse is moved, updateMove is called with the new mouse position. So now mouseX and mouseY will always reflect the current mouse position.

Now we do the loop.

while true do
    wait(0.05)

Next we create the clone. What you did clones the object, but its parent remains nil so it isn't added anywhere. Also, it will be inconsistent potentially since you don't refer to the specific one.

So we're going to clone the label and create a reference to it.

    img = originalImage:Clone()
    img.Position = UDim2.new( 0, mouseX - obj.AbsolutePosition.x - 150  , 0, mouseY - obj.AbsolutePosition.y - 150)
    img.Parent = obj

And then just end the while-loop:

end

And there you go. This should functional like what you expect (though I'm not exactly sure what you expect from this).

All together:

obj = script.Parent
originalImage = obj.Image:Clone()

mouseX = 0
mouseY = 0

-- both of these are defaults, where the mouse is before the player puts their mouse over it.

function updateMove( x, y)
    mouseX = x
    mouseY = y
end

obj.MouseMoved:connect( updateMove )

while true do
    wait(0.05)
    img = originalImage:Clone()
    img.Position = UDim2.new( 0, mouseX - obj.AbsolutePosition.x - 150  , 0, mouseY - obj.AbsolutePosition.y - 150)
    img.Parent = obj
end

EDIT: If you want them to disappear after some time, there are a couple ways to do this. Coroutines are one solution. There are other solutions, but they aren't as neat.

We're going to need some new functions.

function async( f )
    local c = coroutine.create( f ) -- we're creating a coroutine out of the given function `f`
    -- c is local so that we can produce multiple
    coroutine.resume( c ) -- this starts the coroutine
end

Next, we'll take the code for making the new image, and put it in its own function:

function makeImage()
    -- this time it's local, because there will be more than one at once
    local img = originalImage:Clone()
    img.Position = UDim2.new( 0, mouseX - obj.AbsolutePosition.x - 150  , 0, mouseY - obj.AbsolutePosition.y - 150)
    img.Parent = obj
    wait( 15 )
    img:Remove()
end

We want it to run async, so we'll replace that code in the loop with async( makeImage )

All together:

function async( f )
    local c = coroutine.create( f ) -- we're creating a coroutine out of the given function `f`
    -- c is local so that we can produce multiple
    coroutine.resume( c ) -- this starts the coroutine
end


obj = script.Parent
originalImage = obj.Image:Clone()

mouseX = 0
mouseY = 0

-- both of these are defaults, where the mouse is before the player puts their mouse over it.

function makeImage()
    -- this time it's local, because there will be more than one at once
    local img = originalImage:Clone()
    img.Position = UDim2.new( 0, mouseX - obj.AbsolutePosition.x - 150  , 0, mouseY - obj.AbsolutePosition.y - 150)
    img.Parent = obj
    wait( 15 )
    img:Remove()
end


function updateMove( x, y)
    mouseX = x
    mouseY = y
end

obj.MouseMoved:connect( updateMove )

while true do
    wait(0.05)
    async( makeImage )
end