It is Japanese quince, Chaenomeles...There are big differences between Japanese and Chinese Quince.
Japanese quince tends to be a multi-stemmed shrub, while Chinese quince usually has substantial trunks and more tree-like form. You are very unlikely to find Chinese quince , Pseudocydonia, at Home Depot as it tends to be a "specialty" plant sold by nurseries for usually big buck.
Japanese quince is a lot more common, inexpensive and easily produced.
I love my quinces. have 40-50 of them. chinese quince have very pointed leaves. i had to have my friend in california get my first one. They're not all that common to where i would think a retailer other than a specialized nursery would carry.
This is when I usually will give mine a shot of fertilzer for the winter and to help with blooming next spring. No first number but tens and twelves for the last two.
Quince are generally the second bloomer in the spring behind ume (apricot). Ume is in bloom around here generally in january and my chojubai quince ( the best quince in the world) come on in february.
Of all my quinces a hand full are styled in the singular trunk style. I really like cabudachi (clump style).
I have a couple of chinese quinces and, if memory serves me, got them from George Muranaka in California. George sells on ebay and has some nice trees. You may want to check him out. I would really like to be able to visit his nursery.
According to Warren Hill, on the subject of Pseudocydonia chinesis, put it in the ground for a couple of years and I quote: "Feed, feed, feed. Mainly fish emulsion, MorBloom and cottonseed meal. My specimen is over 14 years old and grown from a cutting. Also have three others I layered off.
Now if I just could afford to buy a pot big enough to hold him.