Screw size

That would depend on the side mount, where it was made and who installed it. Can you measure the screw diameter where it comes through the rail on the inside?
Diameter minus .063 and then divide the remainder by 13. That gives you the 'Number' size of the screw UNLESS it's metric. Most likely, it will be a fine thread like 10-32 or 12-28. Those are most common.

Pretty sure they are metric. It was bought to put on a Husqvarna that was drilled for a side mount.

Europe makers adopted 6-48 as sight screw 'standard' before WW-II, but side mounts uses a bigger screw.
Have you got the mount or the gun or both?

Both

Brownell's used to have fairly large kits with assorted screw sizes for bases and rings.

Looking now they still sell some in different sizes. They show ring screws at 8-40, 6-40, and 6-48. We used to trim the correct screw to length, but Brownell's sells quite a few lenths.

Good luck in your quest.

Take a ring into Ace or Tru Value and pick the screws that fit. Rings are usually coarser thread like 6-32 or 6-40 but there is no standard.

I have some no 6 screws here. They won’t even go through the holes. Probably going to try Fastenal.

I can "eyeball" thread pitch from about # 8 on up. Smaller is harder, and metric is (well, metric).
Wonder if the resolution here will help any? I'll try a picture.

Edit May 22: Post and picture are no longer relevant because the screws are now believed to be #4 rather than #6. Picture is taken down.

Disregard.

I think it was Tasco many decades ago that had big clunky-looking scope rings with 5-40 screws hold the lids on. The holes were oversized so there was very little thread doing the holding. I re-tapped to 6-40 without having to drill. 6-40 was Redfield size at the time.

Decided to use calipers on them. Measure .110 0r 2.8 mm or 7/64. I think that makes them a number 4. Just have to figure out what thread now.

4-40 most likely. That's a common electronics screw size, but mighty small in an aluminon part subject to recoil.

So I can probably find them fairly easy. Wonder what my son would say if I took them out of his X-Box? There are 4 per ring which helps a little.