I bought this plant/small tree from a very small nursery specializing in Succulent and Cactus. I absolutely love it, but have no idea what it is.
The leaves almost look like a squash or melon (in fact, that's all that came up when I tried using a Plant Identification App!), it's definitely not.
I've had it for about 3-4 yrs, it's never had any flowers, buds, pods, seeds, or fruit, it just looks like this year round. It's about 3ft from the soil line to the top.
It's a variety of Uncarina species otherwise called Mouse Trap Tree, Succulent Sesame, Unicorn Tree. But I don't know why it's not flowering.
Details here
And here
Photos are copyright on both the sites.
Excerpt from the latter (tubtropicals)
Uncarina grandidieri is a most attractive plant. Deciduous shrub or small tree to 25ft, trunk up to 1ft in diameter. Abundant water when growing, keep on the dry side when dormant.
The flower resembles a large Petunia in form and is bright yellow with a dark throat, as in the Thunbergia alata. The stems are stout and become thickened with age. The hairy leaves resemble those of the cotton plant. They are sticky to the touch and yield a musty odor when rubbed. The leaves are deciduous during the winter resting season. Fruit has small inwardly pointed barbs mounted on 3/4in pedicels. Don't touch this fruit unless you want to spend some time trying to remove it from your fingers.
Looks to me like a variant of the cold climate paw paw, or Babaco. Babaco is deciduous (though may keep leave in warmer climates (not sure about this as i live in a relatively cold climate)).
The one I have in the yard looks slightly larger than this but has a very similar growth habit. I have not seen my one fruit yet. Not sure what climate you are in, so this might help you rule it in or out.
