Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Jackson, Mississippi to Cozumel as you normally would.
Due to multiple factors, expect to potentially pay more when booking in January. For low rates, August can be a great choice for travel to Cozumel. Flights to Cozumel from Jackson, Mississippi in August are about $563 on average during August, but can be found for as low as $279.