The only direct service to to Messina from Catania Fontanarossa airport is the SAIS bus. You can check their daily schedule here: SAIS AUTOLINEE. The last service departs from Catania Airport at 23:00.
Should you miss that last bus, your only option is to hop on an AMT Alibus Service (runs every 25 minutes from 5:00 AM until midnight) to Catania Central Train Station where you can get a train to Messina. The train schedules are available on trenitalia.it.
Our advice is to avoid booking a plane landing late at night in Catania, unless you have a friend/relative who can pick you up. Though trains to Messina are available, oftentimes they might not run until 5:00AM the morning after!
Related post: How to get to Catania Airport from Messina.