Water line won't stay connected to aftermarket freezer port
It is very common in refrigerators to use push-to-connect fittings for joining polypropylene water lines. If that is the kind of connector in use previously, yours appears to be broken (some examples here and here) and the metal ring is likely part of the broken connector.

If the fridge was never sold with an ice maker, then it would have not had any need for a water intake port. Therefore, that part must have been part of the aftermarket kit used. What you may want to consider instead of looking at the model number of the fridge is looking for a model number/manufacturer for the ice maker. If you can find one (you might need to remove a panel or take the ice maker loose to find it) you may be able to use that to track down a replacement part instead.

If you can't find a replacement port, consider just drilling a slightly larger hole in the port and replacing the existing polypropylene line all the way up to the ice maker with a slightly longer water line and use a connector on the outside of the fridge such as this, this, or this. You can usually get replacement polypropylene hoses at home depot or lowes by the foot. You may also be able to find the push-to-connect fittings too - just make sure they are the right size and you don't break the one going into your ice maker too!