I can not find a recipe for quince paste (Membrillo) that you can can however there are many recipes you can google on the net.  It is not a safety issue to make it and refrigerate it for months since quince is high in acid and the paste has lots of sugar and lemon juice.  

As for jam we do have a quince recipe for making quince preserves which is similar to jam. 

Quince Preserves 

2 cups sugar

2 quarts water

7 cups quartered, cored, peeled quince (about 3 pounds before preparing 

Sterilize jars (makes about 4 1/2 pints)

When preparing quince, discard all gritty parts.  Combine sugar and water: boil 5 minutes.  Add quince and cook until fruit has a clear, red color and syrup is almost jelling point, about 1 hour.  As mixture thickens, stir frequently to prevent sticking.  Pour hot preserves into hot jars, leaving 1/4 inch head space.  Wipe jar rims and adjust lids.  Process 5 minutes in a boiling water canner.  

From So Easy To Preserve , University of Georgia Extension Service.

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Nellie Oehler