Typically brown algae, diatoms appear first in a tank. Usually followed by green algae, spot algae. Once the green algae appears the diatoms will die off. If there is not enough light the green algae won't appear and the diatoms will persist. They need almost no light at all.
Maybe you imported some on the fern but most likely they would appear at some point. They feed on the excess nutrients in the tank. They are very interesting little things. Their exoskeleton is essentially glass. There are thousands of kinds and they are found worldwide, everywhere.
Under the right conditions they will practically smother everything else in a tank. They are easily removed with wiping. Otocinclus will eat them. They will clean a tank almost completely in a few days.
Most of the low light plants don't help that much because they grow slowly. Some of the faster growing plants will help suck the nutrients out of the water. It depends on how much light you have.. Try some others, see what will grow.
More water changes and more frequent cleaning will help. What you need is to balance the nutrients in the tank with the plants. So, plant more plants.