Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Syracuse to Havana as you normally would.
These are just IATA (International Air Transport Association) codes. They are used in aviation to identify and differentiate airports. That’s why a Syracuse Hancock Intl Airport to Havana Jose Marti Intl Airport flight would often be abbreviated as a SYR to HAV flight.