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Set Display mode 800, 600, 32
Sync On
Sync Rate 0

Global A As Integer
Global MenuX, MenuY, MOffsetX, MOffsetY As Integer

MenuX = 50 `Menu Positions
MenuY = 50

MOffsetX = 0 ` Menu Offsets for when grabbing the window it doesnt snap the top right back to the mouse position 
MOffsetY = 0

Load Bitmap "Forest Background.bmp", 0
Load Image "Window.png", 2, 1
Sprite 1, MenuX, MenuY, 2
Set Sprite 1, 1, 1

Set Text Opaque

Do 
    
    A = 0
    MenuHandle()
    
    If A = 1
        Set Cursor 0, 30
        Print "Mouse Over Menu"
    Else
        Set Cursor 0, 30
        Print "               "
    EndIf
    Set Cursor 0,0
    Print "         "
    Set Cursor 0,0
    Print MouseX(), " , ", MouseY()
    Print MenuX, " , ", MenuY
    Sync
Loop

Function MenuHandle()
MOffSetX = MouseX()  `+ MenuX
MOffsetY = MouseY() `+ MenuY
    If MouseX() > MenuX AND MouseY() < MenuY + Sprite Height(1) AND MouseX() < MenuX + Sprite Width(1) AND MouseY() > MenuY AND MouseClick() = 1
        Sprite 1, MOffsetX - MenuX , MOffsetY - MenuY , 2
        
        A = 1
    Endif
Endfunction

Set Display mode 800, 600, 32
Sync On
Sync Rate 0

Global A As Integer
Global MenuX, MenuY As Integer

MenuX = 50 `Menu Positions
MenuY = 50

Load Bitmap "Forest Background.bmp", 0
Load Image "Window.png", 2, 1
Sprite 1, MenuX, MenuY, 2
Set Sprite 1, 1, 1

Set Text Opaque

Do 
    
    A = 0
    MenuHandle()
    DebugText()
    
    Sync
Loop

Function DebugText()
    If A = 1
        Set Cursor 0, 30
        Print "Mouse Over Menu"
    Else
        Set Cursor 0, 30
        Print "               "
    EndIf
    Set Cursor 0,0
    Print "         "
    Set Cursor 0,0
    Print MouseX(), " , ", MouseY()
    Print MenuX, " , ", MenuY
EndFunction

Function MenuHandle()
    If MouseX() > MenuX AND MouseY() < MenuY + Sprite Height(1) AND MouseX() < MenuX + Sprite Width(1) AND MouseY() > MenuY AND MouseClick() = 1
        Offset Sprite 1, MouseX(), MouseY()
        Sprite 1, MouseX(),MouseY(), 2
        A = 1
    Endif
Endfunction

Set Display mode 800, 600, 32
Sync On
Sync Rate 0

Global A As Integer
Global MenuX, MenuY As Integer

Rem Added globals.
Global MouseSelect_Active As Boolean
Global MouseSelect_X As Integer
Global MouseSelect_Y As Integer

MenuX = 50 `Menu Positions
MenuY = 50

Load Bitmap "Forest Background.bmp", 0
Load Image "Window.png", 2, 1
Sprite 1, MenuX, MenuY, 2
Set Sprite 1, 1, 1

Set Text Opaque

Do 
    
    A = 0
    MenuHandle()
    DebugText()
    
    Sync
Loop

Function DebugText()
    If A = 1
        Set Cursor 0, 30
        Print "Mouse Over Menu"
    Else
        Set Cursor 0, 30
        Print "               "
    EndIf
    Set Cursor 0,0
    Print "         "
    Set Cursor 0,0
    Print MouseX(), " , ", MouseY()
    Print MenuX, " , ", MenuY
EndFunction

Rem Added code.

Function MenuHandle()
    If MouseX() > MenuX AND MouseY() < MenuY + Sprite Height(1) AND MouseX() < MenuX + Sprite Width(1) AND MouseY() > MenuY AND MouseClick() = 1 Or MouseSelect_Active = 1
        Rem Use this if you want the user to move the window by clicking the window header only.
        Rem MouseY() < MenuY + 35
        
        Rem Get the value to add for the window offset.
        If MouseSelect_Active = 0
            MouseSelect_X = MouseX() - Sprite X(1)
            MouseSelect_Y = MouseY() - Sprite Y(1)
            MouseSelect_Active = 1
        EndIf

        MenuX = MouseX() - MouseSelect_X
        MenuY = MouseY() - MouseSelect_Y
        
        Rem If you don't want your window to go out of the screen, then here is the code.
        If MenuX < 0 Then MenuX = 0
        If MenuX + Sprite Width(1) > Screen Width() Then MenuX = Screen Width() - Sprite Width(1)
        If MenuY < 0 Then MenuY = 0
        If MenuY + Sprite Height(1) > Screen Height() Then MenuY = Screen Height() - Sprite Height(1)
        
        Sprite 1,MenuX,MenuY, 2
        A = 1
    Endif

    If MouseClick() = 0 Then MouseSelect_Active = 0
Endfunction

Sprite 1,50,50,1
Offset Sprite 1,25,25

If MouseSelect_Active = 0
    MouseSelect_X = MouseX() - Sprite X(1)
    MouseSelect_Y = MouseY() - Sprite Y(1)
    MouseSelect_Active = 1
EndIf

Sprite X = 300
Mouse X = 320

Offset = Mouse X - Sprite X
(Offset = 320 - 300)

Position to place the sprite = Mouse X - Offset
(Sprite X = 320 - 20)

Sprite X = 300

As you can see that does not position the sprite to a new location.  So when the loop runs over the code again this is what happens.

Sprite X = 300
Mouse X = 350

Offset = Mouse X - Sprite X
(Offset = 350 - 300)

Position to place the sprite = Mouse X - Offset
(Sprite X = 350 - 20)

Sprite X = 330


Now it moves the sprite at a new location where we want it.  So that is why you have to get the offset value once only.