Like anonymous said, unsalted butter :) For jams, I'd recommend you to make them at home (so you can control the amount of sugar/no sugar at all), or use other alternatives like honey :) If you're worried about allergy to pollen in honey, there's a kind of honey called honeydew honey which is allergy-free because it's not made with the same type of bees that pollinate flowers!
I would say unsalted butter for kids over 1 year old. As for jam - I cant recommend sadly :( think its full of sugar for the little ones