What is this block called?
 

I see it as a curved bow tie. It is similar to drunkard's path, but my drunkard's path template can't be flipped to the other side like this, the center part becomes too thin. Help!

Sorry, no idea what it's name would be. Never seen this block before.

Not sure what the name is, but have seen several quilts in the last few months using the pattern. Seems like "circles" was in the name, obviously. lol Try pinterest.com for circle quilts, bow tie circles, etc.

If you want to try: take your round template and move it off the square until you have the shape, mark where you want the edges of the fabric with tape, but on the template, so that it makes your round piece or template smaller, use the guides of the tape on the edge of the square of fabric and cut your round part. Sorry if I am not explaining clearly.

You could also do what I do with applique pieces: Print the pattern the size you want, glue paper to cereal box, coke box, some kind of thin cardboard. Cut out template. Remember to add seam allowance.

I think it's a double drunkard's path or double path block. I seem to remember it from one of my books.
Yngldy's idea is good. You can mark your current template, or purchase a smaller version that will fit on your square. If you look online you will see that drunkards path templates vary widely in finished block size and how much of a bite is taken out of the square portion.

You got me looking for it and I need to run my errands,lol. I found this, no name, but like the way they used scraps for the bow tie. I will look for name in my quilt encyclopedia when I get back. Looks like an older pattern. http://qisforquilter.com/2009/09/crazy-baseball-quilt/

It looks like they used just the curved part of the template. I haven't seen this block before but I am sure these amazing QB members will come thru for you.

Apple Core or Indian Hatchet. I think that Pepper Cory did some quilts with that template more than a few years ago. More recently, Fons & Porter's magazine had a small feature on it in January/February 2016, don't recall what they called it.

I wanted to find out more about this block and used Google images with the names Apple Core or Indian Hatchet Quilt block. i don't see this block in the results https://www.google.com/search?q=Appl...HZPnCmgQsAQIQA

Thinking of you while running errands. Measure your circle template side without the seam allowance. Double it. That is the size of the square you want to make (plus outside seam allowances). Take a square ruler and draw that size on paper. Place your template on opposite corners and draw shape. If center bow is to your liking, that will be your pattern. If not, add to make the center wider. Make 2 copies. On one draw the seam allowance for the template curve. On the other, draw the seam allowances for the bow. You can adjust to make it look the way you want.

Why not cut your square an inch or three larger, then you can fold in half diagonally, place the 1/4 circle on the corner, and cut out both corners. Would that work? I've never tried the Drunkards Path before so am assuming the pieces will fit. You would have a bit of trimming to do to square up.