It looks like a saprophytic fungal growth - saprophytic fungi are harmless to growing plants, and exist because there's dead (usually woody) material in the soil which they are digesting. I can see some twiggy, or little woody bits in the soil in your cup, and this may be in association with that. If you didn't use new, proprietary seed and cutting compost, this fungus will have been present in whatever soil you did use prior to your putting it in the cup - its just there was some mycelium in the portion in this cup and not in the others. Only water when absolutely necessary to keep the seedling growing - wet soil will increase growth of the fungi exponentially. When the seedling is big enough, (two sets of true leaves) transfer it to another container with fresh potting soil.