I put this in the Pre-1900 thread because the POD will need to be in its early days obviously. So the basic idea is a Vermont Republic, that survives in a completely independent manner into the modern day.
Only way is that constitution convention fails on 1788. But even then there is high odds that New England becomes unified nation. So New York should remain independent. Best case is that every state becomes independent nation. But it might be bit difficult.
In a Balkanized USA smaller states are so much chum for the larger ones. There is no way Vermont could remain independent in the face of a New England Confederation (the most likely outcome). British support would be helpful but it is small, little population, and no resources and difficult to support from Canada in the late 1700s. As mentioned Delaware will undoubtedly go (willingly or not) with Pennsylvania or possibly New Jersey. Many scenarios in fiction have New Jersey being taken over by New York or split between New York and Pennsylvania.
OTL there were numerous overlapping claims on the lands between the Appalachians and the Mississippi among the original 13 colonies. In a Balkanized USA, assuming the British don't grab any of this, you'll see these lands being a case of facts on the ground rather than colonial charters - OTL the US government basically nullified all of these claims in favor of federal sovereignty. Lots of ways these lands could end up divided.