I canned a mustard vinegar sauce that contains granulated sugar and brown sugar plus ketchup. I washed the jars in my dishwasher and cleaned the lids in water and vinegar. Do I need to do anything else after canning the sauce that was held over heat for 30 minutes? Please advise.
Depends how acid it was ("contains vinegar" is not a pH) and what temperature it was "held" at, as well as jar size.
As a rule, canning is best done by following tested recipes and procedures which have been checked to work for the particular food type and jar size - i.e. many things are not considered safe if packed in quarts due to the larger size of the jar, or those that are/can be require more time.
If I guess that you might have boiled/steamed the jars at atmospheric pressure (boiling water bath) that is only an accepted technique for "acid" foods, where "acid" specifically means having a low enough pH to retard botulism growth, not "yep, there's some vinegar in here." One normally attains that by following a tested recipe.
Pressure canning at 15 PSI/1 Bar is required for safety with "low acid" foods. You still need a procedure that ensures that all the contents of the jar get to an adequate temperature for an adequate time to kill botulism spores.
There are many canning procedures that were used, or are being used in some cases (by folks following tradition rather than science) that are not particularly safe. Grandma always doing it this way and not having a known problem is not any guarantee of a safe procedure.