If you run this macro, does it allow you to paste data?

Sub AllowPasteToProtectedSheet()
    Dim TargetRange As Range
    ' Specify the target range where you want to allow pasting
    Set TargetRange = Range("A1:D10") 
    ' Adjust the range as needed
    ' Unprotect the sheet (you may need to set a password)
    ActiveSheet.Unprotect Password:="your_password"
    ' Paste the data into the target range
    TargetRange.PasteSpecial Paste:=xlPasteValuesAndNumberFormats
    ' Protect the sheet again
    ActiveSheet.Protect Password:="your_password", UserInterfaceOnly:=True, AllowFormattingCells:=True, AllowFormattingRows:=True, _
    AllowFormattingColumns:=True, AllowInsertingRows:=True, AllowInsertingColumns:=True, AllowDeletingRows:=True, _
    AllowDeletingColumns:=True, AllowSorting:=True, AllowFiltering:=True, AllowPivotTables:=True
End Sub
I've not tested this, however it I believe that it should. Note after UserInterfaceOnly:= True, the rest are optional ones which may be deleted.