I’m pretty sure we have blackberry jam, but I’m not much of a jam person, so I can’t say so from personal experience. Although if we have the berries, I can’t see why we wouldn’t also have the jam. Looks like blackcurrants is probably what you were thinking of, although they’re technically available in the US now.

https://en.m.wikipedia.org/wiki/Blackcurrant_production_in_the_United_States