It's weeds. I pull them all the time in my garden beds. Most of the time those thin leaves are much thinner than daylily leaves which may make you think they are baby daylilies/new fans, but they are not. Also, you can tell by the roots. If you should happen to pull a daylily, they can be replanted. Daylily roots are not that thin. At least mine aren't. Mine are also more tan to tannish-orange color, too. I typically see new fans sprouting right next to the plant though some cultivars can produce a fan away from the mother plant.
Pull up some of that weed growing in an area away from your daylilies for comparison. And if you have to, dig up a small daylily plant to look at the roots and then replant.
