Sounds like one of two possiblitites. Either pretty early, or put together from two guns. One a JM Marlin, and the other a pre-Marlin Ballard.
The ring lever was the second variation, which is very early, but not the earliest type, as the earliest type levers were those that turned back under, and had either a locating pin on the receiver, or just the hole for a pin. These early levers wer leftovers from Brown that Marlin used up. I have a #4 with such an arrangement, and they are referred to as first variations. The levers look like this:
(You need to Login or Register to view media files and links) None of the JM Marlin marked guns that I know of had the No. 44 marking on the barrels. Some did have the early external extractors, but they did not have the internal automatic extractor in addition. If your barrel is marked No. 44 it's most likely a .44 rimfire chamber, which can also fire .44 centerfire with the reversible Ballard firing pin setup.
If you pull the forearm off, you should find a serial number underneath matching the receiver, but only if it was made by JM Marlin. If it was a pre-Marlin barrel, the serial number will be visable above the wood on the side of the receiver, unless it was removed when installed.
Your lever most likely looks like this one on my #2 in .44Ballard XL.
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