get the most frequently appearing user_code where the month is specified
Just add a WHERE clause:
SELECT user_code, COUNT(invite_code) AS counted
FROM invite_table
WHERE month = 'May' -- or whatever is stored in your varchar(3) column
GROUP BY user_code
ORDER BY counted DESC, user_code -- to break ties in deterministic fashion
LIMIT 10;
You would GROUP BY user_code of course, not by invite_code.
A month column as varchar(3) doesn't seem very useful if there can be data for more than a single year. I would use data type date for it. You can format that any way you like for presentation.