What kind of pepper is this and when will it be "ripe"?
The peppers are a bit larger than a cherry tomato (maybe apricot size).
UPDATE: The peppers turn red after they ripen.
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Peppers easily hybridize so it is possible you may never know, or it might be an obscure variety (My supplier lists 100 or so).
It looks like it is almost certainly a cultivar of Capiscum annuum (as are most cultivated chile peppers).
The closest match to anything I've grown would be Gypsy. This is a small yellow bell pepper that likes warm climates. Size and colour are a good match although they are not as spherical and nobly.
As to when it is ripe? Watch the colours - let a pepper ripen without picking and see where it ends up. You can eat it at any time - remember that green bell peppers and jalapeños are simply unripe peppers! As it ripens, peppers will tend to become sweeter. With yellow peppers, they tend to turn from a green/yellow to a purer yellow. The gypsies turn into more of a lemon yellow shade.