Technically all US half dollars minted from 1794 to 1947 are called Liberty half dollars because they carry various portraits of Miss Liberty.
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The mint mark on Franklin half dollars is on the reverse side, just above the Liberty Bell.
The 1920 Half Dollar - aka - Liberty Walking - mint mark of "D" or "S" would be located on the reverse side, just to the left and above the "H" in half dollar.
The mint mark on a 1936 Walking Liberty half dollar is located on the reverse [tails] side of the coin in the little "valley" just to the left of the word "HALF" near the edge of the rim.
This would be a Liberty Seated half dollar. The mintmark, if it has one, would be locted on the back below the eagle.
Not being certain which half dollar you have, I can tell you that there was never an "A" or a "N" mint mark. The letters you should find will be a "D", an "S", an "O", a "P" or a "CC"