Ron Guth: 1820 Quarter Dollars are divided into two major varieties: Large 0 and Small 0, both referring to the size of the final digit of the date. The Small 0 variety is comprised of the Browning 4 and Browning 5 varieties. For the Large 0 variety, PCGS recognizes Browning 1, Browning 2, and Browning 3. Tompkins (2008) calls Browning 3 a Medium 0, which is justifiable: on the Large 0's, the inside of the 0's is oval in shape; on the Medium 0 and the Small 0's varieties, the right and left sides on the inside of the 0 are straight while the top and bottom are rounded. However, PCGS does not recognize the Medium 0 as a separate major variety.
Here's an attribution guide for 1820 Quarter Dollars:
Large 0 will have Large Stars
Small 0 will have Small Stars
Mediium 0 will have Large Star and a short serif at the top of the 1
Sources and/or recommended reading:
Tompkins, S.M. (2008). Early united states quarters 1796-1838. Sequim, WA: Destni, Inc.
Stack’s 5/1951:438 - Bowers & Merena 1/2001:163 - American Numismatic Rarities 8/2006:409, $80,500 - D. Brent Pogue Collection - Stack’s/Bowers & Sotheby’s 5/2015:1065, $99,875
"Colonel" E.H.R. Green Collection - Partnership of Eric P. Newman & B.G. Johnson (St. Louis Stamp & Coin Co.) - Eric P. Newman, who paid $12.50 - Eric P. Newman Numismatic Education Society - Heritage 11/2013:33341, $41,125