This is a great question. I work with Loving Awareness and Self Inquiry, and I'll share a bit of that here. Technically, what you are talking about is not fear, but anxiety. Fear is the same feeling, but arises when there is a real and obvious cause for the fear. Facing a tiger or a rattlesnake, we want to run. That's fear. But if there is no clear and present danger, then we face anxiety, or stress.
I think anxiety and stress are the deepest problems of Americans today.
Since you mentioned feeling this at bed time, I'll give tips for dealing with anxiety at bedtime and insomnia:
1. Starting about 2 hours before you go to bed, take in no new news. And do not face anything anxious. Rest, relaxation, and gentle exercise and breathing are best. If time doesn't allow that, then work on familiar work. If you are seeking entertainment, choose something nourishing, not thrillers or horror.
2. Stretch well before you go to bed. Even if the fear is emotional, physical relaxation gets it out of the body so you can sleep. Breathe in, and tense an arm or leg, then breathe out, and release the tension.
3. After all is done, and you are ready to sleep, lie in a comfortable position. On your back is best, side is second best. Breathe deeply. Silently, with the breath, say "gentle rest through the night." Breathe and hold this thought (or another nourishing, gentle, peaceful thought) with the breath until you drift off. If you slip up and start feeling anxious, no worries. Just come back to the breath and the gentle words.
We all pick up so much stress during the day. Let's be sure to release it before bed!