Try the following:
update TABLENAME set COLUMN = REPLACE(COLUMN, current substring, new substring)
E.g. The following SQL will replace the substring 'https://m.example.com' to 'https://example.com/m' in column link_content of table me_links.
update me_links set `link_content` = REPLACE(link_content, 'https://m.example.com','https://example.com/m')