Do the snails look like these?
If so, they might be bladder snails. I got these, and the eggs look clear with white dots on them and they are either on the plants or on the walls or filter of a tank i'm cycling. To get rid of the eggs, pluck them out with a siphon or something else and leave them in an empty container, with bad water or without water and after a couple days they should be dead, they will smell bad. Then I just poured it out, or you could throw the container away.
With snails overpopulating it is always due to overfeeding. if you allow them to eat like ghost shrimp, only eating left overs of fish food, they won't overpopulate your tank. I have 2 bladder snails and they are in their own tank and so far ( 2 weeks and a half) they have not made eggs, i'm still checking everynow and then though to be sure.
In the cycling tank, I've been finding snails everywhere because in the beginning I dumped a whole bunch of fish flakes in their for the cycle, they have been eating them all up. If snails eat too much they will get sick and die, so feeding them little doesn't harm them at all.
Though they can overpopulate like crazy, you can control them and they are actually helpful to the tank. They do poo alot.