Don't know what it is called. I would call it a braided star. The center of the quarter square that looks braided would be constructed like a log cabin block, then the half square triangles added on the other corners.
I would start with a 3.5" square, add sides (on 2 sides) with 1.5" strips, then use half-square triangles that would finish at 3" (is that 3 7/8" squares cut diagonally?). That would give you 1/4 of the block. That 1/4 block would finish at 6" (should be 6.5" before sewing to 3 more blocks).