In our New Jersey Recommended list of commercially available native species for landscaping in the state I found the following trees that were about the size you want and all will grow in clay soils. You should look through the New Jersey Recommended list yourself to see if you see any other trees that interest you. You can use the NARROW YOUR SEARCH option to limit the lists to trees by picking "Tree" in the General Appearance slot.
Betula populifolia (Gray birch) is a fast grower and grows to a maximum of 50 feet. Unfortunately, its fast growth also means it is short-lived. Here is more information from Missouri Botanical Garden.
Cercis canadensis (Eastern redbud) has a fast to moderate growth rate and generally grows to 15 feet, but can grow as tall as 30 feet. It has beautiful blossoms in the spring. Here is more information from North Carolina State University and Ohio State University.
Asimina triloba (Pawpaw) grows 10 to 40 feet and will grow in clay soil. Here's more information from Missouri Botanical Garden. It has a medium growth rate according to the University of Connecticul Horticulture.
Fraxinus pennsylvanica (Green ash) grows 50 to 75 feet and will grow in clay soils. Here is more information from Missouri Botanical Garden. It has a fast growth rate according to the University of Connecticut Horticulture.