Without seeing the item I can only make a guess.
Other than Heisey's H in a diamond, the only other H mark that I know anything about would be on look-a-likes and reproduction items from Hsinchu Tiawan, for the A A Importing of St Louis - 1940s-50s
There are three different marks by them that I know of, one is an H in a sideways turned square that many say is an attempt to fake a Heisey's mark, but that would be just too easy to do correctly and the marks side by side are very different looking. Besides that the items produced in Taiwan are nothing like anything Heisey's ever produced. Another mark is the same as above, with a few other elements added and the third mark is an H on its own. Luckily one of these items is found now and then with the red & white paper label still attached and all it says is; "Hsinchu Tiawan" on it. --- Mike