The so-called "Patched 3" is one of the more interestaing varieties among Capped Bust Half Dollars. The variety is actually a die state of Overton 101, which started out as a fairly normal 3, although the top and the bottom halves of the 3 are barely connected. After a certain number of the 1823 O-101 Half Dollars were struck, an engraver took the obverse die and attempted to repair the 3, though the fix came out worse in appearance than the original. The 1823
Patched 3" is known as Overton 101a and, though it is a late state of O-101, it is collected as a completely different variety (this is akin to the 1807 O-111b "Bearded Goddess, which is also a late state of the O-111 dies).
The "Patched 3" Half Dollar is a common variety and can be found in high grade. At least two dozen Mint State examples are known, with the best topping out at MS66.