Your challenge, should you choose to accept it, is to have a Byzantine/Roman/whatever-you-call-them Colony in the New World. Now obviously this requires a Byzantium-survives scenario, but your POD must be after Manzikert. Greek New World colonies are not allowed, nor are parts of the US with large populations of people speaking Greek, nor are successor states to Byzantium such as Trebizond or (arguably) the Ottomans, and definitely not Russian colonies. Restorations of Byzantium (that speak Greek and have their capitals in Constantinople) are allowed.
The colony must last at the very least into the 1700's. Please specify where the colony is located. Bonus points for a short TL, extra bonus points for a summary of the colony's history, going up to at least 1830 or independence from Byzantium.