How do I keep saplings from continually growing in my fence row?

Salt

Do you have just one variety of tree finding it's way into your fence? If so take note what time of year it sends out its seeds/nuts and make sure to get rid of any pesky sprouts early. Also if the saplings are from nuts, beware of squirrels also! I get black walnuts, maple and sumac saplings so I really understand where you're coming from.

Put down a layer of landscape fabric then put mulch over the top of it.

When the seeds blow up along fence line remove them before the open & especially before they germinate(vacuum them up,rake etc.);wet ground thoroughly then hand pull each one removing the whole tap root too don't let them get more than 3-4"s tall it'll be much harder;spray each seedling directly with Round-Up as they begin to grow. If you cut them off it just spreads the root system & they will be harder to remove . If the seeds are from your tree(s) & you can get to them remove them before they fall off/blow off tree so you can control where they are going-Garbage. Trim them off of trees before they even seed, if it's a actually flowering tree do it right after flowers begin to form the seeds.

Thank you for the helpful answers! Will try them.