Don't quite follow- did the screw head break off leaving exposed screw shank or is it flush with the receiver?
Did it break when you were removing it or reinstalling it?
If it broke and left a portion of the shank exposed I would try Kroil or similar, a bit of heat and either vise grips or weld a nut to the stub and slowly back it out.
If it is broken flush with the receiver your only choice is to drill it out.
The hole should be tapped all the way through the receiver, if so center up on the screw and mind the angle of the screw. The Kroil/penetrant again and slowly drill it out, stepping up in drill size as needed. With a little care you can drill it out to where you just barely see the root of the thread then pick out the remnants. You may get lucky and the bit will catch and spin the screw on through and out.
If the hole is not tapped all the way through you can drill it as above or go snag some left handed drill bits and hopefully it will back out.
I would not advise an "ezy-out" on a 1/4" diameter screw. Break it off in the screw and you will discover how expensive EDM work can be.
If it broke when you were reinstalling the screw it is likely cross-threaded. Back it out carefully. With a starting tap you should be able to catch good threads and chase it, if not run the tap in from the interior of the receiver.
1/4-28 TPI
If it is totally munged then Heli-Coils are your friend.
Good luck!