My jasmine plant has tiny like clusters on the stems. Also, it has been invaded by ants and I cannot get rid of them. It is in a pot on my lanai.
I would treat the plant with Neem Oil, this should clear up most infestations of insects.
Here are some links to help you with care information and some ways to deal with ants.
If the ant issue persists, I do recommend a chemical treatment to remove them from the plant. Visit your local garden center for a plant safe ant treatment spray.