When you say "Side mounted scope rail", I'm assuming you mean the kind that slides onto the bracket on the left side of the receiver and locks in place. I use those types on all of my Ak's with no problems at all. I have a normal scope on one, a red dot on another and a holo type site on the third. I have not had any problems at all getting any of them zeroed. There's a couple of possibilties that may be causing you problems.
1...The site that you're using is just not quality enough to withstand the recoil without moving around.
2...The site has a lock system (Maybe) to lock it in after you've sited it in. You're not loosening the lock prior to trying to make adjustments. Usually, on that type of site, the locking screws are in the side and are either tiny Allens or most likely, tiny flat blade screws. (Jewelers screwdrivers)
3...Your scope mount is loose. Slide it on, flip the lever to Lock and see if it moves any at all. The flip lever should have some resistance right at the end before it locks.
4...You're trying to move the bullet impact to the site dot. This is actually a pretty common thing and just means that you've got the site all out of whack.
Here's two methods for zeroing an optical site. First, install the site, remove the cover, spring assembly and bolt. Then block the rifle up with sand bags, etc. so it's steady. If you angle your eyeball just right, you can see down the bore. Line the bore up on a telephone pole, street sign, etc. It should be at least a hundred yards away. While the rifle is mounted steady, adjust the site to match the "bore site". When it's as perfect as you can get it, reassemble the rifle and go to the range.
At the range, block the rifle up on the stand with sand bags, a clamp rest, etc. It should not move or wiggle around. Set up the target at 50 yards. Center the site
exactly at the bullseye and fire one round. Mark the impact hole so you can see it thru the site. (Tape, etc) Now, mount the rifle back steady again and center the site on the bullseye.
Make sure the rifle is mounted steady! Without moving the rifle, adjust the site so the crosshairs, dot, etc. is exactly on the bullet hole. If you did it all correctly, the rifle is now exactly zeroed for that range. Hope this helps. Keep yer powder dry, Mac.
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