Not the fletching. There could be fletching contact too, but that bareshaft shows you have another issue to fix. You would be ahead of the game to skip the paper until you have a bareshaft flying straight IMO. Mark where you rest is currently, move the rest to see if you can get the shaft flying straight. If not, return to original position and go to a lighter shaft or increase weight on the front of your arrow.
I agree with Brock. Get your arrow flying STRAIGHT first, before bothering with paper tuning or rest adjustment... Unless your rest is obviously WAY out of whack. You should be able to eyeball the position of the rest in comparison to the string travel path... close one eye, hold bow so that you're eye is centered with the string, and look "through" to your rest. If the rest is close to where it should be, in line in the center of the string, proceed to bareshaft tuning as Brock suggested first.
Get a good, straight flight of an unfletched arrow via bareshaft tuning. Then, in my opinion, go to walkback tuning instead of messing with paper. Draw a line or hang a vertical string in front of your target. Shoot that line perfectly at like 5 feet away... I mean PERFECTLY... split that sucker. If you miss left or right, adjust your SIGHT accordingly until you split the line. After you split the line at 5 feet, walk-back to 20 yards and try to split the line again. Don't worry about elevation, up/down... Only worry about splitting the line. If you nail it at 20 yards, your centershot of the rest is good. If you miss the line to the left, move the rest just a hair to the right (a little goes a LONG way). Then start the process over... Go back to 5 feet, split the line, adjust the sight if necessary... and then move back to 20 yards again. Repeat until you split the line consistently at both distances. Then, you can move back further, if you
really want to dial it in.
I personally prefer the walk-back tuning method for testing and setting my rest centershot because to me it's quicker and more forgiving than paper-tuning. Paper-tuning can make you chase your tail if your form sucks, or if you torque the grip inconsistently, or even if your release path varies ever so slightly.