What action="store_true" means is that if the argument is given on the command line then a True value should be stored in the parser. What you actually want is to store the given year (as a string) and quarter (as an int).
parser = argparse.ArgumentParser()
parser.add_argument('-q', "--quarter", type=int, help="Enter a Quarter number: 1,2,3, or 4 ")
parser.add_argument('-y', "--year", type=str, help="Enter a year in the format YYYY ")
args = parser.parse_args()
When you specify action='store_true argparse is internally instantiating a _StoreAction instance whose constructor does not accept a type parameter (since it will always be a boolean (True/False)). You cannot supply action="store_true" and ‘type’ at the same time.