This plant finally made some fruit but I have no idea what it is. This one is fuzzy on the surface and about 4 inches long.

A melon of some kind, possibly a cantaloupe.

A search of the internet for "fuzzy little melon green with stripes" turned up images that appear to be a perfect match, including this one of the new fruits. I also found images of many stages of growth.

There are many new fruits on my plant but so far only four have grown past an inch long.

If I'm right, and I'm about 98% sure, it's a BIDWELL CASABA MELON.

It was grown by John Bidwell (1819-1900) a Civil War General and U.S. Senator who procured his stock-seed from the USDA in 1869. An enormous melon, growing 12"-14" long by 9" wide and weighing 12-16 pounds each. Sweet orange flesh, said to “tastes like heavenly orange sherbet.”

It's still a mystery how this one got here in my back yard east of the Mississippi. I've never seen one before but really looking forward to see how large they get and how they taste.

If it is indeed a Bidwell Casaba, then you really lucked out. On the tv one day they had this family in Georgia, that were growing supposedly the worlds best tasting watermelon. They have been doing it for generations. The skin on their melons is so thin, that shipping them for sale is impossible. They would spoil too quick. Would love to taste them. Had an orange watermelon from Texas once that was really good.