What you have there is an Atlas E-Z Seal jar, the last of which was made in the 1960's.
Moreover, it was never intended to be sealed by the twist-on lid from a spaghetti sauce jar.
Since the jar bears the "Mason" name, it probably conforms to the original patent for thread diameter and pitch,
so a set of brand new lids and thread rings will probably work, as Roth and others have suggested. This is, IMO,
the way to go. While you're at the store, buy a case of the smallest (½-pint) wide mouth Mason jars, as suggested.
Great for pipe tobacco aficionados to have on hand.
Some people are compulsive re-purposers, and I can understand that. It's good for the environment too. If you like
doing that sort of thing, I have had success using the jars and original lids from Smuckers™ preserves and jams.