My stud has been bred 4 times this year, all foals were LC and none of the foals were set free, yet it says he has produced 0 Foals and he is also missing from the leaderboards.

I think straws were used to produce those foals

You need to have one LC (non-straw) foal in order to show up on the boards every month :)

Secret my foals are from straws, and they were from 2 game years ago because they were what I got for my secret Santa gift. Not sure about the others but Cora's probably right.

The other two foals he had this year were bred by me livecover, those I know for a fact were LC and were not set free that's why I'm confused.

Both of your studs say 1 foal bred, you probably accidentally used straws. You can check your accountant under Veterinary Fees