What are the circled things called? This is US paper money.

Where did you get the reference to the term radial spandrel?

Yes

Numismatic author William H. Dillistin published an in-depth article "National Bank Notes in the Early Years" in The Numismatist issue of December 1948. "Early years" in this instance meant the Original Series and the Series 1875 notes. His introduction to the "Treasury Numbering System - Series of 1875" included this illustration:

Dillistin called the Bureau of Engraving and Printing's newly added suffix on Series of 1875 nationals a "brace," seen here on the actual notes:

I went to the National Archives to see if I could find any original Treasury or BEP reference to the symbols. Nothing so far but I did see how the Comptroller of the Currency clerks handled the symbols in the National Bank Note receipt and delivery ledgers. For the first delivery of each Series 1875 sheet combination, they recorded the starting serial number showing the "A" prefix, serial number 1, and their own handcrafted version of the "doodad" suffix (below). Unfortunately, while the Comptroller's clerks valiantly replicated the suffix, they never referred to it by name.

Over the years I have occasionally found correspondence at the Archives where Dillistin had written Treasury with various currency questions he had. But whether "brace" was his term or Treasury's we don't know.

I decided to google "What are the symbols before and after serial numbers for 1800's united states currency called?" and discovered the website "uspapermoney.io" that had an article entitled "Symbols in Serial Numbers".www.uspapermoney.io/general/symbols.html

The author depicts 21 different doodads (which the author calls "symbols") and delineates which note uses a specific symbol. The symbols were used to prevent alterations in the serial numbers.

BTW, this is an excellent website that has a great variety of information about US paper money. The site map can be found at this link:uspapermoney.io/general

To read the earlier E-Sylum articles, see:
NOTES FROM E-SYLUM READERS: AUGUST 10, 2025 : What Are These Paper Money Doodads Called? (https://www.coinbooks.org/v28/esylum_v28n32a12.html)
WHAT THOSE PAPER MONEY DOODADS ARE CALLED(https://www.coinbooks.org/v28/esylum_v28n33a11.html)