Like XD said, when you hold a pocket pair and hit your third card on the board, you made a set. Having one of your hole cards show up twice on the board (again, 3 of a kind) is trips. No big deal, just a little pet peeve of mine. Now on to the question. With pocket Jacks, depending on position, players at the table, etc. you should have been able to isolate one or two players with your pre-flop raise or re-raise making it heads-up or three handed going into the flop. Bet strong on the flop since you were the pre flop aggressor and don't be too afraid of callers...some people will chase a draw no matter what. If no club shows on the turn, bet it out again. As long as you were called and not raised after the flop you can be relatively sure your opponent isn't holding a made hand. More than likely after just smooth calling your pre and post-flop raises (which is what will happen in most cases on a board like that) you're going to get another smooth call on the turn due to the odds
the large pot will be laying them. Keep the pressure on with big raises as long as no club comes or other scare card scenario like runner-runner straight cards. If on the turn paint falls, you may want to change up the size of your bet to try and take the pot down immediately. For example, if a Queen falls on the turn and your opponent held A-K with one Club (which some donks play like pocket Aces) he/she has picked up four more outs because of the backdoor straight.
Long story short, hitting a set on the flop is a great way to extract a lot of chips from opponents as long as you don't automatically assume you have it won and bet without considering all of the possible hands your opponent would initially call with, continue calling bets with, etc.