Dear Plattsbburgh Tenant:
So who will sue you, as you claim the landlord is deceased? The landlord is deceased, but you paid rent. Is there a connection between the person who made the claim that the lease required a full fuel tank and the person who took the rent?
If you are sued, the person making the claim must establish the legal right to make the lawsuit. This is known as having "standing." A person or entity with standing must also prove a relation to the person sued. And then that person must prove the underlying claim.
A lease in New York for a definite term may end on a date certain. If the tenancy continues month to month it does so without having to write down or agree on new terms and conditions. As long as the relationship of "landlord" and "tenant" continues, by the process of the tenant remaining in occupancy and paying "rent" the tenancy continues based on the same terms and conditions as were stated in the expired written lease. On the other hand, if the terms and conditions change after the start of the month to month tenancy, such as an agreement that the tank did not have to be topped off, then the burden of proof for that claim shifts to the party opposing the claim that the old written lease controls.
New York State Police frown on someone issuing a check and then making the check bad.
Threats to sue are just that. A threat to sue is not a lawsuit.
You could of course spend some time with a local attorney to determine your rights.
The answer provided to you is in the nature of general information. The general proposition being that you should try to avoid a bad outcome if you can.