Apparently, these are eggs from a parasite inside the body cavity of this Babakina festiva nudibranch. See discussion:
From the gill cavity of a threespined stickleback, not on the gills but attached to the skin.
I am unsure of the identification, but this seems to be the most likely species. It does not look like illustrations of Ergasilus, the only other genus of copepods parasitic on the gills of sticklebacks from our area.
See list of parasites of threespined stickleback from our area at the URI below.