Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Fresno to Puerto Plata 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 Fresno Airterminal Airport to Puerto Plata La Union Airport flight would often be abbreviated as a FAT to POP flight.