1852
Half Cent None made all known pieces are proof restrike made in the late 1850's
1873-CC dime Assume you mean the no arrows coin. Production began but in early Feb 1873 the weight was increased and the coins could not be issued. The unique surviving coin was probably the one sent the annual assay.
1866 quarter, half, and dollar no motto These were fantasy pieces made at a later date for private sale. The quarter and half are unique and there are two of the dollar. A set of these was stolen for DuPont in 1967. Their recover makes an interesting story in itself.
1873-CC quarter, no arrows similar to the 73-CC no arrows dime but apparently a few were released before the Feb weight increase. Five pieces known
1838-O half These were test pieces made to test striking qualities of the new design and then again later in New Orleans to test the die and press (The dies were too short for the press in New Orleans and they tried to compensate by adhering an additional block of steel under the reverse die. It didn't work. About 20 struck, ten in Philadelphia and ten in New Orleans, nine pieces known today.
1853-O half again I am assuming you mean the no arrows coins. Similar to the 1873 CC coins only this time the weights were reduced. Four pieces known , the last one turned up just recently in a group of silver pulled for circulation in the 1930's.
1873-S half, no arrows Similar to the 1873 CC coins, one piece sent to Philadelphia for the annual assay, the rest melted. None known today
1858 dollar Proof only issue Official records say 80 pieces but estimates for frequency of appearance suggest a closer estimate would be 350 pieces.
1870-S dollar In 1870 they laid the cornerstone of the second San Francisco Mint. A complete set of S mint coins were placed in the cornerstone. No coins were made for circulation of the
Half Dime, quarter, silver dollar or three dollar gold. Apparently they struck a few pieces of each of these so they could select a nice one for the cornerstone. The duplicates are where the unique
Half Dime and three dollar gold came from. Not sure why they made so many silver dollars, but nine of these are known today. The 1870 S quarter is the only "cornerstone" piece not known today.
1873-S dollar Assume you mean the Standard dollar. Same as the 1873 S no arrows Half dollar
1841 quarter eagle Not sure
1870-S three dollar gold piece See 70-S dollar
1841-O half eagle not sure
1854-S half eagle First year of issue from the San Francisco mint. They had problems with a shortage of parting acids needed for refining the gold. so mintage was very small.
1861-d $1 Gold The US did not make any gold dollars in Dahlonega before the state succeeded. All coins were struck by the Confederacy but they stopped because there was going to be a shortage of gold and they needed the bullion just for the southern cause.
1875, 1876 $3 Gold In these years the only way to get proof gold was to buy the full set, individual pieces were not sold. That was a HUGE amount of money at the time so mintage dropped through the floor.
1927-d $20 Saint Most of the double eagles struck in the later years never leaft the Treasury vaults. The Treasury did allow collectors to order two coins of each date and and mint for their collections. A few wealthy collectors did purchase examples for their collections and that is where the survivers known today came from.
Wasn't there an actual pattern minted for a half-union? Two different designs in 1877. Several were struck in copper and copper gilt. One specimen of each design was struck in gold. When William Woodin purchased them for $10K each it cause a commotion. In order to get them back the government traded a couple of TRUNKS of patterns for them. today they are in the Smithsonian