To follow Asking the user for input until they give a valid response and using os.path.splitext() to extract the file extension:
import os
ALLOWED_EXTENSTIONS = {".bat", ".exe"}
while True:
    filename = input("Enter file you like to open: ")
    extension = os.path.splitext(filename)[1]
    if extension in ALLOWED_EXTENSTIONS:
        break
with open(filename) as f:
    # do smth with f
Without break:
import os
ALLOWED_EXTENSTIONS = {".bat", ".exe"}
extension = None
while extension not in ALLOWED_EXTENSTIONS:
    filename = input("Enter file you like to open: ")
    extension = os.path.splitext(filename)[1]
with open(filename) as f:
    # do smth with f
Without break and without any imports:
ALLOWED_EXTENSTIONS = (".bat", ".exe")
filename = ""
while not filename.endswith(ALLOWED_EXTENSTIONS):
    filename = input("Enter file you like to open: ")
with open(filename) as f:
    # do smth with f
Without break and without any imports and without endswith():
ALLOWED_EXTENSTIONS = {"bat", "exe"}
filename = ""
while filename.rsplit(".",1)[-1] not in ALLOWED_EXTENSTIONS:
    filename = input("Enter file you like to open: ")
with open(filename) as f:
    # do smth with f