Thankfully my kids were not to fussy.
My DH on the other hand! The only veggies he would eat for years was green beans or corn. He's much better now. He actually tried a brussel sprout the other night. Only took 36 years! Said it wasn't too bad! Of course he didn't like steak when we got married, because the only way his mom ever cooked it was fried, until it was tougher than old shoe leather.
Anyway, I remember when I was a kid and my Mom wanted me to eat things I didn't like. I hated that. A lot of the time, it wasn't so much the taste as it was the texture.
For example, (not veg I know, I liked veggies), as a kid, potato salad and macaroni salad and cole slaw made me gag! Potato/macaroni salad, as a kid, I liked the the individual components, just not all mixed up! Slaw was just weird. The veggie I did not like as a kid was cooked peas. When you stick a fork in them and they squish out all over, could not stand the visual! Looked like an icky green worm!
One thing Mom tried to get me to eat, that I downright refused, and starved was headcheese. It's some gelatinous goo made from the leftovers after home butchering a pig.
Anyway, lots of great suggestions. Creativity, sneak it in, in casseroles and sauces. Ask them why, is it taste, texture, looks? (smooshy peas)
One thing I did when my boys were little and starting to teethe was give them frozen peas and carrots to snack on. I would just give them to them loose on the high chair tray, or sit them down with a small bowl. The cold felt good on the mouth, and they got to do some hand/eye/eating coordination in the process.
Thankfully, as we grow up our tastes do change, I like tater/macaroni salad now. I will eat slaw, but only my recipe.
Keep offering it, try at least one bite, be creative, have patience.