Fair and Square, center inset,
for illustration, upper left
FAIR AND SQUARE is illustrated in Barbara Brackman's ENCYCLOPEDIA OF PIECED QUILT PATTERNS (#2189), and attributed to the Kansas City Star, 1938. Brackman has a very helpful section on these quilt design sources, sometimes with designer names and dates or at least some historical background. Many of the patterns attributed to the KC Star were drafted by Yvonne M. Khin. And this one, or a slight variation at least, is included in Khin's THE COLLECTOR'S DICTIONARY OF QUILT NAMES AND PATTERNS, p.55, also dated 1938.
The illustration upper right, which serves here as the over-all pattern (see tiling below) has a slight variation of additional squares in the corners. There is usually a diamond in the center, but this variation centers on the squares.
As regards the theme, compare at this site with FAIR PLAY but also ON THE SQUARE, both with inspiration from the art of Sonia Delaunay. And for the playful use of "squares" in other titles, see, for example:
SQUARES UPON SQUARES
DOMINO AND SQUARES