SQL standard does not use quotes around numeric literals. MySQL supports them with quotes, but handles them the same as without quotes. Better stick to the standard and not use quotes.
A solution might be to cast the text column to an integer column using the SQL function CAST. Maybe something like this:
SELECT CAST(processID AS INTEGER) AS proc_id, name
FROM processes
ORDER BY proc_id ASC
The CAST type should be INT or INTEGER, but I can't remember which one or if both are accepted by the SQL standard.
Also, you could try to alter the column type to a numeric one. But before you do that, make sure you have a backup of the data.