Give her a flashlight to have in bed with her.
Keep a cup of water in her room, prior to bed.
"Prep" everything prior to bed, in other words, with what she will ask for.
Let her sleep with a Lovey. Or as my daughter does, she likes to make a "nest" as she calls it, and has all her stuffed animals in bed with her. It makes her feel "cozy."
Or, leave on a night-light in her room.
If she wants to "play" tell her no, its bedtime. Keep everything turned OFF, and Dark, and "boring" and quiet. Try not even engaging in talking. Just keep mute.
Or, as my friend did.... when her son was this age, she simply told him "if you want water, you can get it yourself, If you need a light you have a flashlight in your bed" etc.
And for her son, that did the trick.
But, with 3 year olds, yes this is the start of "night time fears." It is developmental... you cannot "turn off" their imaginations, but you can talk to them about it to allay their fears. Fears of the dark or night time, will exist developmentally, even at older ages. But they do honestly get "scared." I remember feeling that way at that age. Its "real" to the child.
If you lay with her until she falls asleep.. that's fine... then gradually move away... meaning, sit in a chair in her room... then nearer and nearer to the door.
Kids, take time to lull asleep. They don't just sleep as soon as their head hits the pillow. Just like adults.
It will take time,
all the best,
Susan