Here is a python script that fetches a popular quote from an API endpoint and appends it to a file:

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import requests

# API endpoint for fetching popular quotes
QUOTE_API_ENDPOINT = 'https://api.quotable.io/random'

# file to append the quote to
QUOTE_FILE = 'quotes.txt'

# fetch a quote from the API endpoint
response = requests.get(QUOTE_API_ENDPOINT)

# parse the response as JSON
quote = response.json()

# extract the quote text from the JSON object
quote_text = quote['content']

# append the quote to the file
with open(QUOTE_FILE, 'a') as f:
    f.write(quote_text)
    f.write('\n')

print(f'Successfully appended quote to {QUOTE_FILE}')

This script uses the requests library to make an HTTP GET request to the API endpoint, which returns a JSON object containing a quote. The script then parses the JSON response and extracts the quote text, and appends it to a file.

Note that this script is just an example and may not work as-is, since it is not connected to a real API endpoint. You will need to provide your own API endpoint and modify the script accordingly.